nLab
algebraic topology

Contents

Idea

Algebraic topology is generally the study of functors from nice categories of spaces to algebraic categories. This is in hindsight, in fact, category theory originally developed out of algebraic topology, where it was used first simply to describe what was going on and then to axiomatise Eilenberg-Steenrod cohomology theories.

References

A textbook with an emphasis on homotopy theory is in

  • Marcelo Aguilar, Samuel Gitler, Carlos Prieto, Algebraic topology from a homotopical viewpoint, Springer (2002) (pdf)

Lecture notes include

Brief indications of open questions and future directions (as of 2013) of algebraic topology and stable homotopy theory are in

Further online resources include

Revised on March 7, 2014 08:09:48 by Urs Schreiber (89.204.139.248)