On homotopy nilpotency of some suspended spaces

Abstract

A homological criterium from [Golasiński, M., On homotopy nilpotency of loop spaces of Moore spaces, Canad. Math. Bull. (2021), 1–12] is applied to investigate the homotopy nilpotency of some suspended spaces. We investigate the homotopy nilpotency of the wedge sum and smash products of Moore spaces M (A, n) with n ≥ 1. The homotopy nilpotency of homological spheres are studied as well.

Keywords

• abelian group
• cartesian product
• homology sphere
• nilpotency class
• n-fold commutator map
• h-space
• loop space
• moore space
• locatiozation
• samelson product
• smash product
• suspension space
• wedge sum
• whitehead product