bibliography for groupoids and algebraic topology


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

0.1 Algebraic Topology and Groupoids

  1. 1.

    Ronald Brown: Topology and Groupoids, BookSurge LLC (2006).

  2. 2.

    Ronald Brown R, P.J. Higgins, and R. Sivera.: “Non-AbelianMathworldPlanetmathPlanetmath algebraic topology”. http://www. bangor.ac.uk/mas010/nonab-a-t.html; http://www.bangor.ac.uk/mas010/nonab-t/partI010604.pdf , Springer: in press (2010).

  3. 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. 4.

    R. Brown and J.-L. Loday: Van Kampen TheoremsMathworldPlanetmath for diagrams of spaces, TopologyMathworldPlanetmath, 26: 311-337 (1987).

  5. 5.

    R. Brown and G. H. Mosa: Double algebroids and crossed modules of algebroids, University of Wales-Bangor, Maths Preprint, 1986.

  6. 6.

    R. Brown and C.B. Spencer: Double groupoidsPlanetmathPlanetmathPlanetmath and crossed modules, Cahiers Top. Géom. Diff. 17 (1976), 343-362.

  7. 7.

    Madalina (Ruxi) Buneci.: Groupoid RepresentationsPlanetmathPlanetmathPlanetmathPlanetmath., Ed. Mirton: Timisoara (2003).

  8. 8.

    Allain Connes: Noncommutative GeometryPlanetmathPlanetmath, Academic Press 1994.

0.2 Non-Abelian Algebraic Topology and Higher Dimensional Algebra

  1. 1.

    Ronald Brown: Non-Abelian Algebraic Topology, vols. I and II. 2010. (in press: Springer): http://www.bangor.ac.uk/ mas010/rbrsbookb-e040310.pdfNonabelian Algebraic Topology:filtered spaces, crossed complexes, cubical higher homotopy groupoids

  2. 2.

    http://en.wikipedia.org/wiki/Higher_dimensional_algebraHigher Dimensional Algebra: An Introduction

  3. 3.

    http://en.wikipedia.org/wiki/User:Bci2/Books/Higher_Dimensional_AlgebraHigher Dimensional Algebra and Algebraic Topology., 282 pages, Feb. 10, 2010

0.2.1 General Topology

  1. 1.

    N. Bourbaki, General Topology, Part 1, Addison-Wesley Publishing Company, 1966

  2. 2.
  3. 3.

    R. Engelking, General topology, PWN, Warsaw, 1977.

  4. 4.

    R. Brown, Elements of Modern Topology, McGraw Hill, Maidenhead, 1968.

  5. 5.

    R. Brown and T.L. Thickstun, Low-Dimensional Topology, Volume 1 of the conference on Topology in Low DimensionMathworldPlanetmath, Bangor, 1979), London Math. Soc. Lecture Notes No. 48 (1982). (now available from CUP).

  6. 6.

    R.Brown, Topology: a geometric account of general topology, homotopy typesMathworldPlanetmath, and the fundamental groupoidMathworldPlanetmathPlanetmathPlanetmath, Ellis Horwood, Chichester (1988) 460 pp.

  7. 7.

    J.L. Kelley, General Topology, D. van Nostrand Company, Inc., 1955; Springer-Verlag, New York, ISBN 0-387-90125-6

  8. 8.
  9. 9.

    William S. Massey, A Basic Course in Algebraic Topology, Springer, New York, 1991; ISBN 0-387-97430-X, 3-540-97430-X; QA612.M374

  10. 10.

    C.R.F. Maunder, Algebraic Topology, Cambridge University Press, 1980, Dover Edition, 1996; ISBN 0-486-69131-4.

  11. 11.

    Fred H. Croom, Basic ConceptsMathworldPlanetmath of Algebraic Topology, Springer-Verlag, New York, 1978; ISBN 0-387-90288-0

  12. 12.

    Joseph J. Rotman, An Introduction to Algebraic Topology, Springer-Verlag, New York, 1988: ISBN 0-387-96678-1

0.3 Topology in relation to other areas of mathematics*

  1. 1.

    Michael Atiyah, The Geometry and Physics of Knots, Cambridge University Press, Cambridge, 1990; ISBN 0-521-39521-6, 0-521-39554-2

  2. 2.

    Alfsen, E.M. and F. W. Schultz: Geometry of State SpacesMathworldPlanetmath of Operator Algebras, Birkhäuser, Boston-Basel-Berlin (2003).

  3. 3.

    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.

  4. 4.

    M. Chaician and A. Demichev: Introduction to Quantum GroupsPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath, World Scientific (1996).

0.4 Topological Groups*

  1. 1.
  2. 2.

References on the Foundations of AlgebraPlanetmathPlanetmath: Groups, Rings, Fields, Modules,… , MSC 20-00, MSC 20A

  1. 1.

    David S. Dummit, Richard M. Foote, Abstract Algebra, John Wiley and Sons, Inc. 1999

  2. 2.

    I. N. Herstein, Topics in Algebra, Xerox College Publishing, 1975.

    A classic undergraduate textbook introducing groups, rings, fields, and linear algebra.

  3. 3.

    Serge Lang, Algebra, Addison-Wesley Publishing Company, 1997.

    A textbook covering a broad range of topics in algebra, such as basic homological algebra and basic category theoryMathworldPlanetmathPlanetmathPlanetmath which are covered at the beginner’s level.

  4. 4.

    John S. Rose, A Course on Group Theory, Dover Publications, New York, 1994.

  5. 5.

    Thomas W. Hungerford, Algebra, Springer-Verlag Graduate Texts in Mathematics 73, 1974.

0.5 Literature on Groupoids and Topology

  1. 1.

    R. Brown, K.Hardie, H.Kamps, T. Porter, The homotopy double groupoidPlanetmathPlanetmath of a Hausdorff space, Theory and Applications of Categories, 10 (2002) 71-93.

  2. 2.

    R. Brown, I.Icen and O. Mucuk. Holonomy and monodromyMathworldPlanetmath groupoidsPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath, in Lie Algebroids, Banach Center Publications Institute of Mathematics, Polish Academy of Sciences, Warsaw, 54 (2001) 9-20.

  3. 3.

    R. Brown. Algebraic homotopy, Supplement III., in Encyclopaedia of Mathematics, Managing Editor: M. Hazewinkel Kluwer Academic Publishers (2002) 29-31.

  4. 4.

    R. Brown. Exponential law in topology, Supplement III., in Encyclopaedia of Mathematics, Managing Editor: M. Hazewinkel Kluwer Academic Publishers (2002) 142-143.

  5. 5.

    R. Brown İ. Içen, and O. Mucuk), Examples and coherence properties of local subgroupoids, Topology and its Applications 127 (2003) 393-408.

  6. 6.

    R. Brown and I.ICEN. Towards a 2-dimensional notion of holonomy, Advances in Math. 178 (2003) 141-175.

  7. 7.

    R. Brown C.D.WENSLEY), Computation and homotopical applications of induced crossed modules, J. Symbolic ComputationMathworldPlanetmathPlanetmath 35 (2003) 59-72.

  8. 8.

    R. Brown, M. BULLEJOS and T.PORTER), Crossed complexes, free crossed resolutions and graph products of groups, Proceedings Workshop Korea 2000, Heldermann Verlag. 27 (2003) 11-26.

0.6 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 TheoryMathworldPlanetmath, 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 CategoryMathworldPlanetmath: A Survey of the AnalogiesMathworldPlanetmath 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.

0.6.1 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 TheoryMathworldPlanetmath New York, NY: Springer-Verlag, 1977.

Firby, P.A. and Gardiner, C.F. SurfaceMathworldPlanetmath 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.

0.6.2 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 AlgebraicPlanetmathPlanetmath Approach, New York, NY: Academic Press, 1982.

Giblin, P.J. Graphs, Surfaces and HomologyMathworldPlanetmathPlanetmath: 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 PointsMathworldPlanetmathPlanetmath of Complex HypersurfacesMathworldPlanetmath 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 GroupsMathworldPlanetmath, 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.

0.6.3 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 DifferentiablePlanetmathPlanetmath 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 GroupsMathworldPlanetmath New York, NY: Springer-Verlag, 1983.

Title bibliography for groupoids and algebraic topology
Canonical name BibliographyForGroupoidsAndAlgebraicTopology
Date of creation 2013-03-22 18:15:50
Last modified on 2013-03-22 18:15:50
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 41
Author bci1 (20947)
Entry type Bibliography
Classification msc 55Q05
Classification msc 55U40
Classification msc 20L05
Classification msc 58H05
Classification msc 54-00
Classification msc 58H10
Classification msc 22A22
Classification msc 18B40
Classification msc 20-00
Classification msc 55-00
Synonym algebraic topology bibliography
Related topic BibliographyOfCategoryTheory