Are two finite $H$-spaces homotopy equivalent?

Abstract

This paper proposes an algorithm that decides if two simply connected spaces represented by finite simplicial sets of finite $k$-type and finite dimension $d$ are homotopy equivalent. If the spaces are homotopy equivalent, the algorithm finds a homotopy equivalence between their Postnikov stages in dimension $d$. As a consequence, we get an algorithm deciding if two spaces represented by finite simplicial sets are stably homotopy equivalent.

Minor changes. Accepted in JTA. arXiv admin note: substantial text overlap with arXiv:2105.10443

References in corpus (1)

• Algorithmic aspects of homeomorphism problems