Tori Detect Invertibility of Topological Field Theories
Algebraic Topology
2018-06-13 v2
Abstract
A once-extended d-dimensional topological field theory Z is a symmetric monoidal functor (taking values in a chosen target symmetric monoidal (infty,2)-category) assigning values to (d-2)-manifolds, (d-1)-manifolds, and d-manifolds. We show that if Z is at least once-extended and the value assigned to the (d-1)-torus is invertible, then the entire topological field theory is invertible, that is it factors through the maximal Picard infty-category of the target. Results are obtained in the presence of arbitrary tangential structures.
Keywords
Cite
@article{arxiv.1511.01772,
title = {Tori Detect Invertibility of Topological Field Theories},
author = {Christopher Schommer-Pries},
journal= {arXiv preprint arXiv:1511.01772},
year = {2018}
}
Comments
33 pages, 4 figures; added application to Crane-Yetter TQFTs