User:Bci2/Subpage/BooksNotable

Notable Algebraic Topologists v.2, p.229, Edited by Bci2

Algebraic Topology

Algebraic topology

Topology

Glossary of topology

Algebraic Topologists

Frank Adams

Michael Atiyah(Sir Michael Francis Atiyah, OM, FRS, FRSE)

Ronald Brown (mathematician)

Karol Borsuk

Luitzen Egbertus Jan Brouwer

William Browder

Nicolas Bourbaki

Henri Cartan

Samuel Eilenberg

Peter Freyd

Mikhail Gromov

Alexander Grothendieck

Heinz Hopf

Michael J. Hopkins

Witold Hurewicz

Maxim Kontsevich

Otto Hermann Künneth

Saunders Mac Lane

J.P. May

John Coleman Moore

Sergei Petrovich Novikov

Daniel Quillen

Jean-Pierre Serre

Dennis Sullivan

René Thom

Hassler Whitney

J. H. C. Whitehead

Important Theorems in Algebraic Topology

Borsuk-Ulam theorem

Brouwer fixed point theorem

Cellular approximation theorem

Eilenberg–Zilber theorem

Hurewicz theorem

Kunneth theorem

Poincaré duality theorem

Universal coefficient theorem

Van Kampen's theorem

Whitehead's theorem

Important publications in algebraic topology

List of publications in mathematics#Algebraic topology

See also

Higher dimensional algebra

Higher category theory

Van Kampen's theorem

Groupoid

Lie groupoid

Lie algebroid

Grothendieck topology

Serre spectral sequence

Sheaf

Homotopy theory

Fundamental group

Fundamental groupoid

Homology theory

Homological algebra

Cohomology theory

K-theory

Algebraic K-theory

TQFT

Homotopy quantum field theory(HQFT)

References cited

[Generalized van Kampen's theorems

• Bredon, Glen E. (1993), Topology and Geometry, Graduate Texts in Mathematics 139, Springer, ISBN 0-387-97926-3, retrieved 2008-04-01.
• Hatcher, Allen (2002), Algebraic Topology, Cambridge: Cambridge University Press, ISBN 0-521-79540-0. A modern, geometrically flavored introduction to algebraic topology.
• Maunder, C.R.F. (1970), Algebraic Topology, London: Van Nostrand Reinhold, ISBN 0-486-69131-4.

R. Brown and A. Razak, ``A van Kampen theorem for unions of non-connected spaces'', Archiv. Math. 42 (1984) 85-88.

[[P.J. Higgins, Categories and groupoids (1971) Van Nostrand-Reinhold.]

[[Ronald Brown, Higher dimensional group theory (2007) (Gives a broad view of higher dimensional van Kampen theorems involving multiple groupoids).]]

E. R. van Kampen. ''On the connection between the fundamental groups of some related spaces.'' American Journal of Mathematics, vol. 55 (1933), pp. 261–267.

[[Ronald Brown, Higgins, P. J. and R. Sivera. 2007, vol. 1 Non-Abelian Algebraic Topology: filtered spaces, crossed complexes, cubical higher homotopy groupoids; downloadable PDF:]

• "Van Kampen's theorem". PlanetMath.
• "Van Kampen's theorem result". PlanetMath.

Ronald Brown R, K. Hardie, H. Kamps, T. Porter T.: The homotopy double groupoid of a Hausdorff space., ''Theory Appl. Categories'', '''10''':71–-93 (2002).

• [[Dylan G.L. Allegretti, Simplicial Sets and van Kampen's Theorem (Discusses generalized versions of van Kampen's theorem applied to topological spaces and simplicial sets).]]

Important publications in algebraic topology

Higher homotopy, generalized van Kampen's theorem]]

[[ http://en.wikipedia.org/wiki/User:Bci2/Books/Algebraic_Topology GNUL Textbook on Algebraic Topology vol.1] ]]

Bibliography