A geometric description of the Atiyah-Hirzebruch spectral sequence for B-bordism

TL;DR

This paper provides a geometric framework for understanding the Atiyah-Hirzebruch spectral sequence in B-bordism using bordism classes of maps from stratifolds, including a computational example and generalizations to other homology theories.

Contribution

It introduces a geometric description of the spectral sequence's terms and differentials for B-bordism, extending to general homology theories via Postnikov sections.

Findings

Geometric description of spectral sequence terms and differentials

Illustrative computational example included

Extension to general homology theories using Postnikov sections

Abstract

In this paper we give a geometric description of the general term and the differential of the Atiyah-Hirzebruch spectral sequence for $B$-bordism. This description is given in terms of bordism classes of maps from stratifolds. We illustrate that with a computational example. We also discuss the case of a general homology theory, where this description is given in terms of the Postnikov sections of the given theory.