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Notable Algebraic Topologists v.2, p.229, Edited by Bci2
[edit]- 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
Wikimedia Commons has media related to Algebraic topology.
- 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:]
- [[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[1]]]
- [[ http://en.wikipedia.org/wiki/User:Bci2/Books/Algebraic_Topology GNUL Textbook on Algebraic Topology vol.1][2] ]]
- Bibliography
- ^ R. Brown, K.A. Hardie, K.H. Kamps and T. Porter, A homotopy double groupoid of a Hausdorff space, Theory and Applications of Categories. 10 (2002) 71-93. http://www.emis.de/journals/TAC/volumes/14/9/14-09.pdf
- ^ I.C. Baianu et al. Algebraic Topology, Category Theory and Higher Dimensional Algebra (v.2 and 3.), 485 pages, June 17, 2009 Preprint. http://planetphysics.org/?op=getobj&from=books&id=266