Talk:PlanetPhysics/Bibliography for Groupoids and Algebraic Topology

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The following are recent sources for several areas in \htmladdnormallink{abstract algebra}{http://planetphysics.us/encyclopedia/PAdicMeasure.html},

homological algebra, \htmladdnormallink{homotopy groups}{http://planetphysics.us/encyclopedia/ExtendedHurewiczFundamentalTheorem.html}, \htmladdnormallink{homotopy}{http://planetphysics.us/encyclopedia/ThinEquivalence.html} \htmladdnormallink{groupoids}{http://planetphysics.us/encyclopedia/GroupoidHomomorphism2.html}, \htmladdnormallink{algebraic topology}{http://planetphysics.us/encyclopedia/NoncommutativeGeometry4.html} and \htmladdnormallink{higher dimensional algebra}{http://planetphysics.us/encyclopedia/2Groupoid2.html} (\htmladdnormallink{HDA}{http://planetphysics.us/encyclopedia/2Groupoid2.html}).

\subsection{Algebraic Topology and Groupoids} \begin{enumerate} \item Ronald Brown: Topology and Groupoids, BookSurge LLC (2006). \item Ronald Brown R, P.J. Higgins, and R. Sivera.: \emph{``Non-Abelian algebraic topology"}, . http://www. bangor.ac.uk/mas010/nonab-a-t.html; http://www.bangor.ac.uk/mas010/nonab-t/partI010604\htmladdnormallink{.pdf}{http://planetphysics.us/encyclopedia/LebesgueMeasure.html} (in preparation), (2008). \item R. Brown and J.-L. Loday: \htmladdnormallink{homotopical excision}{http://planetphysics.us/encyclopedia/CubicalHigherHomotopyGroupoid.html}, and \htmladdnormallink{Hurewicz theorems}{http://planetphysics.us/encyclopedia/ModuleAlgebraic.html}, for n-cubes of spaces, Proc. London Math. Soc., 54:(3), 176-192, (1987). \item R. Brown and J.-L. Loday: \htmladdnormallink{Van Kampen theorems}{http://planetphysics.us/encyclopedia/VanKampenTheorems.html} for \htmladdnormallink{diagrams}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} of spaces, Topology, 26: 311-337 (1987). \item R. Brown and G. H. Mosa: \htmladdnormallink{double algebroids}{http://planetphysics.us/encyclopedia/GeneralizedSuperalgebras.html} and \htmladdnormallink{crossed modules}{http://planetphysics.us/encyclopedia/CubicalHigherHomotopyGroupoid.html} of \htmladdnormallink{algebroids}{http://planetphysics.us/encyclopedia/Algebroids.html}, University of Wales-Bangor, Maths Preprint, 1986. \item R. Brown and C.B. Spencer: \htmladdnormallink{double groupoids}{http://planetphysics.us/encyclopedia/WeakHomotopy.html} and crossed modules, Cahiers Top. G\'eom. Diff. 17 (1976), 343-362. \item Madalina (Ruxi) Buneci.: \emph{\htmladdnormallink{groupoid representations}{http://planetphysics.us/encyclopedia/GroupRepresentations.html}}., Ed. Mirton: Timisoara (2003). \item Allain Connes: \emph{\htmladdnormallink{noncommutative geometry}{http://planetphysics.us/encyclopedia/NoncommutativeGeometry4.html}}, Academic Press 1994. \end{enumerate}

\subsection{Non-Abelian Algebraic Topology and Higher Dimensional Algebra} \begin{enumerate} \item Ronald Brown: \htmladdnormallink{non-Abelian algebraic topology}{http://planetphysics.us/encyclopedia/ModuleAlgebraic.html}, vols. I and II. 2010. (in press: Springer): \htmladdnormallink{Nonabelian Algebraic Topology:filtered spaces, crossed complexes, cubical higher homotopy groupoids}{http://www.bangor.ac.uk/~mas010/rbrsbookb-e040310.pdf}

\item \htmladdnormallink{Higher Dimensional Algebra: An Introduction}{http://en.wikipedia.org/wiki/Higher_dimensional_algebra}

\item \htmladdnormallink{Higher Dimensional Algebra and Algebraic Topology., 282 pages, Feb. 10, 2010}{http://en.wikipedia.org/wiki/User:Bci2/Books/Higher_Dimensional_Algebra}

\end{enumerate} \subsubsection{General Topology} \begin{enumerate} \item N. Bourbaki, \emph{General Topology, Part 1}, Addison-Wesley Publishing Company, 1966 \item John G. Hocking, Gail S. Young, \emph{Topology, Addison-Wesley, Reading, Massachussets, 1961; Dover, New York, 1988; ISBN 0-486-65674, QA611.H68} \item R.~Engelking, \emph{General topology}, PWN, Warsaw, 1977. \item R. Brown, \emph{Elements of Modern Topology}, McGraw Hill, Maidenhead, 1968. \item R. Brown and T.L. Thickstun, \emph{Low-Dimensional Topology}, \htmladdnormallink{volume}{http://planetphysics.us/encyclopedia/Volume.html} 1 of the conference on Topology in Low Dimension, Bangor, 1979), London Math. Soc. Lecture Notes No. 48 (1982). (now available from CUP). \item R.Brown, \emph{Topology: a geometric account of general topology, homotopy \htmladdnormallink{types}{http://planetphysics.us/encyclopedia/Bijective.html}, and the \htmladdnormallink{fundamental groupoid}{http://planetphysics.us/encyclopedia/CubicalHigherHomotopyGroupoid.html}}, Ellis Horwood, Chichester (1988) 460 pp. \item J.L. Kelley, \emph{General Topology}, D. van Nostrand Company, Inc., 1955; Springer-Verlag, New York, ISBN 0-387-90125-6 \item William J. Pervin, \emph{Foundations of General Topology, Academic Press, New York, 1964.} \item William S. Massey, \emph{A Basic Course in Algebraic Topology}, Springer, New York, 1991; ISBN 0-387-97430-X, 3-540-97430-X; QA612.M374 \item C.R.F. Maunder, \emph{Algebraic Topology}, Cambridge University Press, 1980, Dover Edition, 1996; ISBN 0-486-69131-4. \item Fred H. Croom, \emph{Basic \htmladdnormallink{concepts}{http://planetphysics.us/encyclopedia/PreciseIdea.html} of Algebraic Topology}, Springer-Verlag, New York, 1978; ISBN 0-387-90288-0 \item Joseph J. Rotman, \emph{An Introduction to Algebraic Topology}, Springer-Verlag, New York, 1988: ISBN 0-387-96678-1 \end{enumerate}

\subsection{Topology in relation to other areas of mathematics*}

\begin{enumerate} \item Michael Atiyah, \emph{The Geometry and Physics of Knots}, Cambridge University Press, Cambridge, 1990; ISBN 0-521-39521-6, 0-521-39554-2 \item Alfsen, E.M. and F. W. Schultz: \emph{\htmladdnormallink{geometry of state spaces}{http://planetphysics.us/encyclopedia/QuantumOperatorAlgebra4.html} of \htmladdnormallink{operator algebras}{http://planetphysics.us/encyclopedia/Groupoid.html}}, Birkh\"auser, Boston-Basel-Berlin (2003). \item J. Butterfield and C. J. Isham : A \htmladdnormallink{topos}{http://planetphysics.us/encyclopedia/GrothendieckTopos.html} perspective on the \htmladdnormallink{Kochen-Specker theorem}{http://planetphysics.us/encyclopedia/QAT2.html} I-IV, Int. J. Theor. Phys, 37 (1998) No 11., 2669-2733 38 (1999) No 3., 827-859, 39 (2000) No 6., 1413-1436, 41 (2002) No 4., 613-639. \item M. Chaician and A. Demichev: \emph{Introduction to Quantum \htmladdnormallink{groups}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html}}, World Scientific (1996). \end{enumerate}

\subsection{Topological Groups*}

\begin{enumerate} \item Taqdir Husain, \emph{Introduction to Topological Groups, W. B. Saunders Company, Philadelphia, 1966.} \item Markus Stroppel, \emph{Locally Compact Groups, EMS Textbooks in Mathematics, European Mathematical Society, Z\"urich, 2006, ISBN 3-03719-016-7} \end{enumerate}

{\bf References on the Foundations of Algebra: Groups, Rings, Fields, Modules,... , MSC 20-00, MSC 20A}

\begin{enumerate} \item David S. Dummit, Richard M. Foote, \emph{Abstract Algebra}, John Wiley and Sons, Inc. 1999 \item I. N. Herstein, \emph{Topics in Algebra}, Xerox College Publishing, 1975. \begin{quote} A classic undergraduate textbook introducing groups, rings, fields, and linear algebra. \end{quote} \item Serge Lang, \emph{Algebra}, Addison-Wesley Publishing Company, 1997. \begin{quote}A textbook covering a broad range of topics in algebra, such as basic homological algebra and basic category theory which are covered at the beginner's level. \end{quote} \item John S. Rose, \emph{A Course on Group Theory}, Dover Publications, New York, 1994. \item Thomas W. Hungerford, \emph{Algebra}, Springer-Verlag Graduate Texts in Mathematics {\bf 73}, 1974. \end{enumerate}

\subsection{Literature on Groupoids and Topology}

\begin{enumerate} \item R. Brown, K.Hardie, H.Kamps, T. Porter, The homotopy double groupoid of a Hausdorff space, \emph{Theory and Applications of Categories}, {\bf 10} (2002) 71-93. \item R. Brown, I.Icen and O. Mucuk. Holonomy and monodromy groupoids, in \emph{Lie Algebroids}, Banach Center Publications Institute of Mathematics, Polish Academy of Sciences, Warsaw, {\bf 54} (2001) 9-20. \item R. Brown. Algebraic homotopy, Supplement III., in \emph{Encyclopaedia of Mathematics}, Managing Editor: M. Hazewinkel Kluwer Academic Publishers (2002) 29-31. \item R. Brown. Exponential law in topology, Supplement III., in \emph{Encyclopaedia of Mathematics}, Managing Editor: M. Hazewinkel Kluwer Academic Publishers (2002) 142-143. \item R. Brown \.I. I\c{c}en, and O. Mucuk), Examples and coherence properties of local subgroupoids, \emph{Topology and its Applications} {\bf 127} (2003) 393-408. \item R. Brown and I.ICEN. Towards a 2-dimensional notion of holonomy, \emph{Advances in Math}. {\bf 178} (2003) 141-175. \item R. Brown C.D.WENSLEY), Computation and homotopical applications of induced crossed modules, \emph{J. Symbolic Computation} {\bf 35} (2003) 59-72. \item R. Brown, M. BULLEJOS and T.PORTER), Crossed complexes, free crossed resolutions and graph products of groups, \emph{Proceedings Workshop Korea 2000}, Heldermann Verlag. {\bf 27} (2003) 11-26. \end{enumerate}

\subsection{General Topology}

Alexandroff, Paul. Elementary Concepts of Topology Mineola, NY: Dover, 1961.

Arkhangelski i, A.V. and Pontrjagin, Lev S., eds. General Topology I: Basic Concepts and Constructions, Dimension Theory New York, NY: Springer-Verlag, 1990.

Bing, R.H. Elementary Point Set Topology Washington, DC: Mathematical Association of America, 1960.

Bourbaki, Nicolas. Elements of Mathematics: General Topology New York, NY: Springer-Verlag, 1989.

Chinn, William G. and Steenrod, Norman E. First Concepts of Topology Washington, DC: Mathematical Association of America, 1966.

Dugundji, James. Topology Boston, MA: Allyn and Bacon, 1966.

Fuks, D.B. and Rokhlin, V.A. Beginner's Course in Topology: Geometric Chapters New York, NY: Springer-Verlag, 1984.

Gamelin, Theodore W. and Greene, Robert E. Introduction to Topology Philadelphia, PA: Saunders College, 1983.

Gemignani, Michael C. Elementary Topology, Mineola, NY: Dover, 1990. Second Edition.

Hausdorff, Felix. Set Theory, New York, NY: Chelsea, 1957, 1978. Third Edition.

Hurewicz, Witold and Wallman, Henry. Dimension Theory Princeton, NJ: Princeton University Press, 1941.

Kaplansky, Irving. Set Theory and Metric Spaces, New York, NY: Chelsea, 1977. Second Edition.

Kelley, John L. General Topology, New York, NY: Springer-Verlag, 1975.

Kuratowski, K. Topology, New York, NY: Academic Press, 1966, 1969. 2 Vols.

Munkres, James R. Topology: A First Course Englewood Cliffs, NJ: Prentice Hall, 1975.

Newman, M.H.A. Elements of the Topology of Plane Sets of Points New York, NY: Cambridge University Press, 1964.

Oxtoby, John C. Measure and Category: A Survey of the Analogies between Topological and Measure Spaces, New York, NY: Springer-Verlag, 1980. Second Edition.

Sierpinski, W. General Topology Toronto: University of Toronto Press, 1952.

Simmons, George F. Introduction to Topology and Modern Analysis Melbourne, FL: Robert E. Krieger, 1983.

Steen, Lynn Arthur and Seebach, J. Arthur, Jr. Counterexamples in Topology, New York, NY: Springer-Verlag, 1978. Second Edition.

Sutherland, W.A. Introduction to Metric and Topological Spaces New York, NY: Clarendon Press, 1975.

Willard, Stephen. General Topology Reading, MA: Addison-Wesley, 1970.

\subsubsection{Geometric Topology and Theoretical Physics}

Atiyah, Michael F. The Geometry and Physics of Knots New York, NY: Cambridge University Press, 1990. Burde, Gerhard and Zieschang, Heiner. Knots Hawthorne, NY: Walter de Gruyter, 1985.

Crowell, Richard H. and Fox, Ralph H. Introduction to Knot Theory New York, NY: Springer-Verlag, 1977.

Firby, P.A. and Gardiner, C.F. Surface Topology New York, NY: Ellis Horwood, 1982.

Flegg, H. Graham. From Geometry to Topology Philadelphia, PA: Crane, Russak, 1974.

Francis, George K. A Topological Picturebook New York, NY: Springer-Verlag, 1987.

Freedman, M.H. and Luo, Feng. Selected Applications of Geometry to Low-Dimensional Topology Providence, RI: American Mathematical Society, 1990.

Griffiths, H.B. Surfaces, New York, NY: Cambridge University Press, 1976, 1981. Second Edition.

Kauffman, Louis H. On Knots Princeton, NJ: Princeton University Press, 1987.

Moise, Edwin E. Geometric Topology in Dimensions 2 and 3 New York, NY: Springer-Verlag, 1977.

Montesinos, Jose Maria. Classical Tessellations and Three-Manifolds New York, NY: Springer-Verlag, 1987.

Reidemeister, K. Knot Theory Moscow, ID: BCS Associates, 1983.

Rolfsen, Dale. Knots and Links, Boston, MA: Publish or Perish, 1976, 1991. Second Edition.

Rourke, C.P. and Sanderson, B.J. Introduction to Piecewise-Linear Topology New York, NY: Springer-Verlag, 1972.

Wall, C.T.C. A Geometric Introduction to Topology Reading, MA: Addison-Wesley, 1972.

Weeks, Jeffrey R. The Shape of Space: How to Visualize Surfaces and Three-Dimensional Manifolds New York, NY: Marcel Dekker, 1985.

\subsubsection{Algebraic Topology}

Aleksandrov, P. Combinatorial Topology, Baltimore, MD: Graylock Press, 1956--60. 3 Vols.

Armstrong, M.A. Basic Topology New York, NY: Springer-Verlag, 1983, 1990.

Artin, Emil. Introduction to Algebraic Topology Columbus, OH: Charles E. Merrill, 1969.

Blackett, Donald W. Elementary Topology: A Combinatorial and Algebraic Approach, New York, NY: Academic Press, 1982.

Giblin, P.J. Graphs, Surfaces and Homology: An Introduction to Algebraic Topology, New York, NY: Chapman and Hall, 1981. Second Edition.

Gramain, Andre. Topology of Surfaces Moscow, ID: BCS Associates, 1984.

Greenberg, Marvin Jay and Harper, John R. Lectures on Algebraic Topology, Reading, MA: W.A. Benjamin, 1967, 1981. Second Edition.

Henle, Michael. A Combinatorial Introduction to Topology New York, NY: W.H. Freeman, 1979.

Janich, Klaus. Topology New York, NY: Springer-Verlag, 1984.

Kosniowski, Czes. A First Course in Algebraic Topology New York, NY: Cambridge University Press, 1980.

Lefschetz, Solomon. Topology, New York, NY: Chelsea, 1956. Second Edition.

Massey, William S. Algebraic Topology: An Introduction New York, NY: Springer-Verlag, 1977.

Massey, William S. A Basic Course in Algebraic Topology New York, NY: Springer-Verlag, 1991.

Milnor, John W. Singular Points of Complex Hypersurfaces Princeton, NJ: Princeton University Press, 1968.

Milnor, John W. and Stasheff, James D. Characteristic Classes Princeton, NJ: Princeton University Press, 1974.

Munkres, James R. Elements of Algebraic Topology Reading, MA: Addison-Wesley, 1984.

Naber, Gregory L. Topological Methods in Euclidean Spaces New York, NY: Cambridge University Press, 1980.

Pontrjagin, Lev S. Topological Groups, New York, NY: Gordon and Breach, 1966. Second Edition.

Pontrjagin, Lev S. Foundations of Combinatorial Topology Baltimore, MD: Graylock Press, 1952.

Seifert, Herbert and Threlfall, W. A Textbook of Topology New York, NY: Academic Press, 1980.

Spanier, Edwin H. Algebraic Topology New York, NY: McGraw-Hill, 1966.

Stillwell, John. Classical Topology and Combinatorial Group Theory New York, NY: Springer-Verlag, 1980.

Vick, James. Homology Theory: An Introduction to Algebraic Topology New York, NY: Academic Press, 1973.

\subsubsection{Differential Topology}

Almgren, F.J. Plateau's Problem Redwood City, CA: Benjamin Cummings, 1966.

Auslander, Louis and Mackenzie, Robert E. Introduction to Differentiable Manifolds Mineola, NY: Dover, 1977.

Brocker, Th. and Janich, Klaus. Introduction to Differential Topology New York, NY: Cambridge University Press, 1982.

Chillingworth, D.R.J. Differential Topology with a View to Applications Brooklyn, NY: Pitman, 1976.

Guillemin, Victor and Pollack, Alan. Differential Topology Englewood Cliffs, NJ: Prentice Hall, 1974.

Hirsch, Morris W. Differential Topology New York, NY: Springer-Verlag, 1976.

Milnor, John W. Topology from the Differentiable Viewpoint Charlottesville, VA: University Press of Virginia, 1965.

Milnor, John W. Morse Theory Princeton, NJ: Princeton University Press, 1963.

Singer, I.M. and Thorpe, John A. Lecture Notes on Elementary Topology and Geometry New York, NY: Springer-Verlag, 1987.

Warner, Frank W. Foundations of Differentiable Manifolds and Lie Groups New York, NY: Springer-Verlag, 1983.

See Also: bibliography for category theory

Cross-references: quantum groups, topos, operator, knots, geometry, fundamental groupoid, homotopy types, dimension, volume, elements, Bourbaki, non-Abelian, noncommutative geometry, groupoid representations, double groupoids, modules, diagrams, theorems, HTML, groupoids, higher dimensional algebra, topology, algebraic, homotopy groupoids, homotopy groups, algebra, areas, sources

Classifications: AMS MSC: 55-00 (Algebraic topology :: General reference works ) 20-00 (Group theory and generalizations :: General reference works ) 18B40 (Category theory; homological algebra :: Special categories :: Groupoids, semigroupoids, semigroups, groups ) 22A22 (Topological groups, Lie groups :: Topological and differentiable algebraic systems :: Topological groupoids ) 58H10 (Global analysis, analysis on manifolds :: Pseudogroups, differentiable groupoids and general structures on manifolds :: Cohomology of classifying spaces for pseudogroup structures ) 54-00 (General topology :: General reference works ) 58H05 (Global analysis, analysis on manifolds :: Pseudogroups, differentiable groupoids and general structures on manifolds :: Pseudogroups and differentiable groupoids) 20L05 (Group theory and generalizations :: Groupoids ) 55U40 (Algebraic topology :: Applied homological algebra and category theory :: Topological categories, foundations of homotopy theory) 55Q05 (Algebraic topology :: Homotopy groups :: Homotopy groups, general; sets of homotopy classes)

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