nLab
algebraic topology

Contents

Idea

Algebraic topology is generally the study of functors from nice categories of spaces to algebraic categories. This can be considered, from the nPOV, as closely related to higher category theory. 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. There has been considerable convergence of the two subjects, not only in methodology, but in aims and motivations.

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 September 14, 2014 07:26:15 by Tim Porter (2.26.35.200)