Interactions of strings and equivariant homology theories

TL;DR

This paper introduces a new geometric construction called the space of parallel strings with labels, which leads to a method for creating equivariant homology theories from partial monoids.

Contribution

It presents a novel geometric approach to constructing equivariant homology theories using spaces of labeled strings and partial monoids.

Findings

Defined the space of parallel strings with partially summable labels

Constructed a machinery to produce equivariant homology theories from partial monoids

Provided a geometric interpretation of group completion for particle spaces

Abstract

We introduce the notion of the space of parallel strings with partially summable labels, which can be viewed as a geometrically constructed group completion of the space of particles with labels. We utilize this to construct a machinery which produces equivariant generalized homology theories from such simple and abundant data as partial monoids.