PlanetPhysics/Bibliography for Groupoids and Algebraic Topology

The following are recent sources for several areas in abstract algebra, homological algebra, homotopy groups, homotopy groupoids, algebraic topology and higher dimensional algebra (HDA).

Algebraic Topology and Groupoids

 * 1) Ronald Brown: Topology and Groupoids, BookSurge LLC (2006).
 * 2) Ronald Brown R, P.J. Higgins, and R. Sivera.: Non-Abelian algebraic topology, . http://www. bangor.ac.uk/mas010/nonab-a-t.html; http://www.bangor.ac.uk/mas010/nonab-t/partI010604.pdf (in preparation), (2008).
 * 3) R. Brown and J.-L. Loday: homotopical excision, and Hurewicz theorems, for n-cubes of spaces, Proc. London Math. Soc., 54:(3), 176-192, (1987).
 * 4) R. Brown and J.-L. Loday: Van Kampen theorems for diagrams of spaces, Topology, 26: 311-337 (1987).
 * 5) R. Brown and G. H. Mosa: double algebroids and crossed modules of algebroids, University of Wales-Bangor, Maths Preprint, 1986.
 * 6) R. Brown and C.B. Spencer: double groupoids and crossed modules, Cahiers Top. Géom. Diff. 17 (1976), 343-362.
 * 7) Madalina (Ruxi) Buneci.: groupoid representations., Ed. Mirton: Timisoara (2003).
 * 8) Allain Connes: noncommutative geometry, Academic Press 1994.

Non-Abelian Algebraic Topology and Higher Dimensional Algebra

 * 1) Ronald Brown: non-Abelian algebraic topology, vols. I and II. 2010. (in press: Springer): Nonabelian Algebraic Topology:filtered spaces, crossed complexes, cubical higher homotopy groupoids


 * 1) Higher Dimensional Algebra: An Introduction


 * 1) Higher Dimensional Algebra and Algebraic Topology., 282 pages, Feb. 10, 2010

General Topology
Addison-Wesley Publishing Company, 1966 Ellis Horwood, Chichester (1988) 460 pp. D. van Nostrand Company, Inc., 1955; Springer-Verlag, New York, ISBN 0-387-90125-6 New York, 1964.}
 * 1) N. Bourbaki, General Topology, Part 1 ,
 * 1) John G. Hocking, Gail S. Young, Topology, Addison-Wesley, Reading, Massachussets, 1961; Dover, New York, 1988; ISBN 978-0486656762, QA611.H68
 * 2) R.~Engelking, General topology, PWN, Warsaw, 1977.
 * 3) R. Brown, Elements of Modern Topology, McGraw Hill, Maidenhead, 1968.
 * 4) R. Brown and T.L. Thickstun, Low-Dimensional Topology, volume 1 of the conference on Topology in Low Dimension, Bangor, 1979), London Math. Soc. Lecture Notes No. 48 (1982). (now available from CUP).
 * 5) R.Brown, Topology: a geometric account of general topology, homotopy types, and the fundamental groupoid},
 * 1) J.L. Kelley, General Topology ,
 * 1) William J. Pervin, \emph{Foundations of General Topology, Academic Press,
 * 1) William S. Massey, A Basic Course in Algebraic Topology, Springer, New York, 1991; ISBN 0-387-97430-X, 3-540-97430-X; QA612.M374
 * 2) C.R.F. Maunder, Algebraic Topology, Cambridge University Press, 1980, Dover Edition, 1996; ISBN 0-486-69131-4.
 * 3) Fred H. Croom, Basic concepts of Algebraic Topology, Springer-Verlag, New York, 1978; ISBN 0-387-90288-0
 * 4) Joseph J. Rotman, An Introduction to Algebraic Topology, Springer-Verlag, New York, 1988: ISBN 0-387-96678-1

Topology in relation to other areas of mathematics*
operator algebras}, Birkhäuser, Boston-Basel-Berlin (2003).
 * 1) Michael Atiyah, The Geometry and Physics of Knots, Cambridge University Press, Cambridge, 1990; ISBN 0-521-39521-6, 0-521-39554-2
 * 2) Alfsen, E.M. and F. W. Schultz: \htmladdnormallink{geometry of state spaces {http://planetphysics.us/encyclopedia/QuantumOperatorAlgebra4.html}  of
 * 1) J. Butterfield and C. J. Isham : A topos perspective on the Kochen-Specker theorem 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.
 * 2) M. Chaician and A. Demichev: Introduction to Quantum groups, World Scientific (1996).

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

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

A classic undergraduate textbook introducing groups, rings, fields, and linear algebra. 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.
 * 1) David S. Dummit, Richard M. Foote, Abstract Algebra, John Wiley and Sons, Inc. 1999
 * 2) I. N. Herstein, Topics in Algebra, Xerox College Publishing, 1975.
 * 1) Serge Lang, Algebra, Addison-Wesley Publishing Company, 1997.
 * 1) John S. Rose, A Course on Group Theory, Dover Publications, New York, 1994.
 * 2) Thomas W. Hungerford, Algebra, Springer-Verlag Graduate Texts in Mathematics {\mathbf 73}, 1974.

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

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.

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.

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.

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)