Modelling and Computing Homotopy Types: I

Abstract

The aim of this article is to explain a philosophy for applying higher dimensional Seifert-van Kampen Theorems, and how the use of groupoids and strict higher groupoids resolves some foundational anomalies in algebraic topology at the border between homology and homotopy. We explain some applications to filtered spaces, and special cases of them, while a sequel will show the relevance to n-cubes of pointed spaces.

29 pages, v2 additional references and minor corrections v3 section 1 changed. more references. other minor changes. v3 minor corrections. To aqppear in a special issue of Idagationes Math. in honor of L.E.J. Brouwer to appear in 2017