Abstract
A once extended –dimensional topological field theory is a symmetric monoidal functor (taking values in a chosen target symmetric monoidal –category) assigning values to –manifolds, –manifolds, and –manifolds. We show that if is at least once extended and the value assigned to the –torus is invertible, then the entire topological field theory is invertible, that is, it factors through the maximal Picard –category of the target. Similar results are shown to hold in the presence of arbitrary tangential structures.
Citation
Christopher J Schommer-Pries. "Tori detect invertibility of topological field theories." Geom. Topol. 22 (5) 2713 - 2756, 2018. https://doi.org/10.2140/gt.2018.22.2713
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