Cobordism invariants from BPS q-series

TL;DR

This paper explores how BPS q-series invariants depend on additional structures like Spin$^c$ structures, and how different limits and summations yield various cobordism invariants.

Contribution

It demonstrates how to derive homology cobordism invariants from BPS q-series by analyzing limits and summations over Spin$^c$ structures.

Findings

Different limits of the BPS q-series produce distinct cobordism invariants.

Summing over Spin$^c$ structures yields new homology cobordism invariants.

The approach connects BPS invariants with topological cobordism classifications.

Abstract

Many BPS partition functions depend on a choice of additional structure: fluxes, Spin or Spin$^c$ structures, etc. In a context where the BPS generating series depends on a choice of Spin$^c$ structure we show how different limits with respect to the expansion variable $q$ and different ways of summing over Spin$^c$ structures produce different invariants of homology cobordisms out of the BPS $q$-series.