bibliography for groupoids and algebraic topology

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).

0.1

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 ,
Springer: in press (2010).

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.

0.2

Non-Abelian Algebraic Topology and Higher Dimensional Algebra

1.

Ronald Brown: Non-Abelian Algebraic Topology, vols. I and II. 2010. (in press: Springer):

http://www.bangor.ac.uk/ mas010/rbrsbookb-e040310.pdf

Nonabelian Algebraic Topology:

filtered spaces

, crossed complexes, cubical higher homotopy groupoids

2.

http://en.

wikipedia

.org/wiki/Higher_dimensional_algebra

Higher Dimensional Algebra: An

Introduction

3.

http://en.wikipedia.org/wiki/User:Bci2/Books/Higher_Dimensional_Algebra

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

0.2.1

General Topology

1.

N.

Bourbaki

,

General Topology, Part 1

,
Addison-Wesley Publishing Company, 1966

2.

3.

R. Engelking,

General topology

, PWN, Warsaw, 1977.

4.

R. Brown,

Elements of Modern Topology

, McGraw Hill, Maidenhead, 1968.

5.

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).

6.

R.Brown,

Topology: a geometric account of general topology,

homotopy types

, and the

fundamental groupoid

,
Ellis Horwood, Chichester (1988) 460 pp.

7.

J.L. Kelley,

General Topology

,
D. van Nostrand Company, Inc., 1955; Springer-Verlag, New York, ISBN 0-387-90125-6

8.

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.

C.R.F. Maunder,

Algebraic Topology

, Cambridge University Press, 1980, Dover Edition, 1996; ISBN 0-486-69131-4.

11.

Fred H. Croom,

Basic

Concepts

of Algebraic Topology

, Springer-Verlag, New York, 1978; ISBN 0-387-90288-0

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.

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:

Geometry of

State Spaces

of
Operator Algebras

, Birkhäuser, Boston-Basel-Berlin (2003).

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.

M. Chaician and A. Demichev:

Introduction to

Quantum Groups

, World Scientific (1996).

0.4

Topological Groups*

1.

2.

References

on the

Foundations

of

Algebra

: Groups, Rings, Fields, Modules,… , MSC 20-00, MSC 20A

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.

A classic undergraduate textbook introducing groups, rings, fields, and

linear algebra

.

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 theory

which are covered at the beginner’s level.

4.

John S. Rose,

A Course on

Group Theory

, Dover Publications, New York, 1994.

5.

Thomas W. Hungerford,

Algebra

, Springer-Verlag Graduate Texts in Mathematics

73

, 1974.

0.5

Literature on Groupoids and Topology

1.

R. Brown, K.Hardie, H.Kamps, T. Porter, The

homotopy double groupoid

of a

Hausdorff space

,

Theory and Applications of Categories

,

10

(2002) 71-93.

2.

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,

54

(2001) 9-20.

3.

R. Brown. Algebraic homotopy, Supplement III., in

Encyclopaedia of Mathematics

, Managing Editor: M. Hazewinkel Kluwer Academic Publishers (2002) 29-31.

4.

R. Brown. Exponential law in topology, Supplement III., in

Encyclopaedia of Mathematics

, Managing Editor: M. Hazewinkel Kluwer Academic Publishers (2002) 142-143.

5.

R. Brown İ. Içen, and O. Mucuk), Examples and coherence properties of local subgroupoids,

Topology and its Applications

127

(2003) 393-408.

6.

R. Brown and I.ICEN. Towards a 2-dimensional notion of holonomy,

Advances in Math

.

178

(2003) 141-175.

7.

R. Brown C.D.WENSLEY),

Computation

and homotopical applications of induced crossed modules,

J.

Symbolic Computation

35

(2003) 59-72.

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 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.

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 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.

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

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.

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

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.

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

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