# 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

* Ronald Brown: Topology and Groupoids, BookSurge LLC (2006).
* 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).
* 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).
* R. Brown and J.-L. Loday: Van Kampen theorems for diagrams of spaces, Topology, 26: 311-337 (1987).
* R. Brown and G. H. Mosa: double algebroids and crossed modules of algebroids, University of Wales-Bangor, Maths Preprint, 1986.
* R. Brown and C.B. Spencer: double groupoids and crossed modules, Cahiers Top. Géom. Diff. 17 (1976), 343-362.
* Madalina (Ruxi) Buneci.: groupoid representations., Ed. Mirton: Timisoara (2003).
* Allain Connes: noncommutative geometry, Academic Press 1994.

### Non-Abelian Algebraic Topology and Higher Dimensional Algebra

* 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
* Higher Dimensional Algebra: An Introduction
* Higher Dimensional Algebra and Algebraic Topology., 282 pages, Feb. 10, 2010

#### General Topology

* N. Bourbaki, General Topology, Part 1 ,
Addison-Wesley Publishing Company, 1966
* John G. Hocking, Gail S. Young, Topology, Addison-Wesley, Reading, Massachussets, 1961; Dover, New York, 1988; ISBN 978-0486656762, QA611.H68
* R.~Engelking, General topology , PWN, Warsaw, 1977.
* R. Brown, Elements of Modern Topology , McGraw Hill, Maidenhead, 1968.
* 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).
* R.Brown, Topology: a geometric account of general topology, homotopy types , and the fundamental groupoid},
Ellis Horwood, Chichester (1988) 460 pp.
* J.L. Kelley, General Topology ,
D. van Nostrand Company, Inc., 1955; Springer-Verlag, New York, ISBN 0-387-90125-6
* William J. Pervin, \emph{Foundations of General Topology, Academic Press,
New York, 1964.}
* William S. Massey, A Basic Course in Algebraic Topology , Springer, New York, 1991; ISBN 0-387-97430-X, 3-540-97430-X; QA612.M374
* C.R.F. Maunder, Algebraic Topology , Cambridge University Press, 1980, Dover Edition, 1996; ISBN 0-486-69131-4.
* Fred H. Croom, Basic concepts of Algebraic Topology, Springer-Verlag, New York, 1978; ISBN 0-387-90288-0
* 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*

* Michael Atiyah, The Geometry and Physics of Knots , Cambridge University Press, Cambridge, 1990; ISBN 0-521-39521-6, 0-521-39554-2
* Alfsen, E.M. and F. W. Schultz: \htmladdnormallink{geometry of state spaces {http://planetphysics.us/encyclopedia/QuantumOperatorAlgebra4.html} of
operator algebras}, Birkhäuser, Boston-Basel-Berlin (2003).
* 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.
* M. Chaician and A. Demichev: Introduction to Quantum groups, World Scientific (1996).

### Topological Groups*

* Taqdir Husain, Introduction to Topological Groups, W. B. Saunders Company, Philadelphia, 1966.
* Markus Stroppel, \emph{Locally Compact Groups, EMS Textbooks in Mathematics, European Mathematical Society,
Z\"urich, 2006, ISBN 3-03719-016-7}
{\mathbf References on the Foundations of Algebra: Groups, Rings, Fields, Modules,... , MSC 20-00, MSC 20A}
* David S. Dummit, Richard M. Foote, Abstract Algebra , John Wiley and Sons, Inc. 1999
* I. N. Herstein, Topics in Algebra , Xerox College Publishing, 1975.
   A classic undergraduate textbook introducing groups, rings, fields, and linear algebra.
* 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 theory which are covered at the beginner's level.
* John S. Rose, A Course on Group Theory , Dover Publications, New York, 1994.
* Thomas W. Hungerford, Algebra , Springer-Verlag Graduate Texts in Mathematics {\mathbf 73}, 1974.

### Literature on Groupoids and Topology

* R. Brown, K.Hardie, H.Kamps, T. Porter, The homotopy double groupoid of a Hausdorff space,
Theory and Applications of Categories , {\mathbf 10} (2002) 71-93.
* 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.
* R. Brown. Algebraic homotopy, Supplement III., in Encyclopaedia of Mathematics , Managing Editor: M. Hazewinkel Kluwer Academic Publishers (2002) 29-31.
* R. Brown. Exponential law in topology, Supplement III., in Encyclopaedia of Mathematics , Managing Editor: M. Hazewinkel Kluwer Academic Publishers (2002) 142-143.
* R. Brown \.I. I\cen, and O. Mucuk), Examples and coherence properties of local subgroupoids, Topology and its Applications {\mathbf 127} (2003) 393-408.
* R. Brown and I.ICEN. Towards a 2-dimensional notion of holonomy, Advances in Math . {\mathbf 178} (2003) 141-175.
* R. Brown C.D.WENSLEY), Computation and homotopical applications of induced crossed modules, J. Symbolic Computation {\mathbf 35} (2003) 59-72.
* 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)