The second homotopy group in terms of colorings of locally finite models and new results on asphericity

Abstract

We describe the second homotopy group of any CW-complex $K$ by analyzing the universal cover of a locally finite model of $K$ using the notion of $G$-coloring of a partially ordered set. As applications we prove a generalization of the Hurewicz theorem, which relates the homotopy and homology of non-necessarily simply-connected complexes, and derive new results on asphericity for two-dimensional complexes and group presentations.

We split our previous paper arXiv:1212.6442v1 into two parts and improved the presentation. The first part is now arXiv:1212.6442v2 and deals with coverings and the fundamental group. This is the second part and deals with the second homotopy group and asphericity

References in corpus (1)

• $G$-colorings of posets, coverings and presentations of the fundamental group

Cited by in corpus (1)

• On homology of finite topological spaces