Periods for topological circle actions

TL;DR

This paper explores the application of Harvey-Lawson currents and sparks to study Hopkins-Singer Wu classes through equivariant Tate K-theory, linking geometric topology with distributional zeta functions.

Contribution

It introduces a novel approach using currents and sparks to analyze Wu classes in the context of circle actions and equivariant K-theory.

Findings

Establishes connections between currents, sparks, and Wu classes.

Proposes a framework for distributional zeta functions in geometric topology.

Abstract

The language of Harvey-Lawson currents and sparks may be useful for the study of Hopkins-Singer Wu classes in geometric topology, via equivariant Tate $K$-theory of circle actions and distributional generalizations of classical zeta functions.