Are two H-spaces homotopy equivalent? An algorithmic view point

Abstract

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