When are two spaces homotopy equivalent?

TL;DR

This paper explores the algorithmic conditions under which two finite simplicial complexes are homotopy equivalent, utilizing Postnikov towers and effective homology to formulate these criteria.

Contribution

It introduces a novel algorithmic framework for determining homotopy equivalence based on Postnikov towers and effective homology.

Findings

Established necessary and sufficient conditions for homotopy equivalence

Developed an algorithmic approach using Postnikov towers

Enhanced understanding of computational topology methods

Abstract

This paper investigates sufficient and necessary conditions for the existence of a homotopy equivalence between two finite simplicial complexes from an algorithmic point of view. As a result, the conditions are formulated in terms of the underlying data of Postnikov towers for simplicial sets with so-called effective homology.