In English

Short Course on Algebraic Topology

(Gliwice, Poland, 3.9.2007)

Lecturer

Martin Fluch

Content

This (very) short course on Algebraic Topology shall give an introduction to some essenetial concepts of this field of mathematics: the fundamental group and homology theories. As an example we will show how those results are used to prove that the Euclidean spaces Rⁿ and R^m are not homeomorphic if n is not equal to m, which is not possible to prove in a purely topological way.

This short lecture will be part of the 3rd Summer School of Algebra and Topology which is held in Gliwice, Poland from 3rd to 7th of September.

Lecture Notes

The notes to the lecture can be downloaded here: alg_top_intro.pdf

Literature

• Fred Croom. Basic Concepts of Algebraic Topology. Undergraduate Texts in Mathematics. Springer-Verlag, 1978.

• Glen Bredon. Topology and Geometry. Graduate texts in mathematics. Springer-Verlag, 1993.

• Jean Dieudonne, A History of Algebraic and Differential Topology 1900-1960, Birkhäuser, 1998.

• Samuel Eilenberg and Norman Steenrod. Foundations of Algebraic Topology. Princton University Press, 1952.

• Allen Hatcher. Algebraic Topology. Cambridge University Press, 2002.
  This book can be downloaded freely from the author's homepage.

• William S. Massey. A Basic Course in Algebraic Topology, Springer-Verlag, 1991.

• Jon May. A Concise Course in Algebraic Topology. University Of Chicago Press, 1999.
  This book can be downloaded freely from the author's homepage.

• Edwin Spanier. Algebraic Topology. Springer-Verlag, 2nd edition, 1966.