Highly divisible cycles in homological Atiyah-Hirzebruch spectral sequences

TL;DR

This paper investigates the structure of certain elements in the Atiyah-Hirzebruch spectral sequence related to a homology theory, focusing on their divisibility properties in the context of CW-complexes.

Contribution

It introduces a detailed analysis of highly divisible cycles within the spectral sequence, revealing new structural insights about their orders and behavior.

Findings

Identification of maximal order elements in spectral sequence groups

Characterization of divisibility properties of cycles in the spectral sequence

Insights into the structure of homological Atiyah-Hirzebruch spectral sequences

Abstract

Let $F_*$ be a homology theory of finite type and $\{E^r_{s,t}(X)=\frac{Z^r_{s,t}(X)}{B^r_{s,t}(X)}; d^r_{s,t}\}$ denote the Atiyah-Hirzebruch spectral sequence for $F_*$ of a $CW$-complex $X$. In this paper we study elements of the maximal possible order in the groups $E^2_{n,0}(X)/Z^{r}_{n,0}(X)$.