Cobordism invariants from BPS q-series

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.

30 pages, 4 figures