A geometric decomposition of spaces into cells of different types

TL;DR

This paper introduces CW(A)-complexes, a generalized form of CW-complexes, extending classical homotopy theory results to a broader class of geometric spaces.

Contribution

It develops the theory of CW(A)-complexes, generalizing CW-complexes and classical results like Whitehead Theorem to new geometric contexts.

Findings

Generalization of CW-complexes to CW(A)-complexes

Extension of Whitehead Theorem to CW(A)-complexes

Deeper understanding of homotopy properties in generalized spaces

Abstract

We develop the theory of CW(A)-complexes, which generalizes the classical theory of CW-complexes, keeping the geometric intuition of J.H.C. Whitehead's original theory. We obtain this way generalizations of classical results, such as Whitehead Theorem, which allow a deeper insight in the homotopy properties of these spaces.