On invertible 2-dimensional framed and $r$-spin topological field theories
Abstract
We classify invertible 2-dimensional framed and -spin topological field theories by computing the homotopy groups and the -invariant of the corresponding bordism categories. The zeroth homotopy group of a bordism category is the usual Thom bordism group, the first homotopy group can be identified with a Reinhart vector field bordism group, or the so called SKK group as observed by Ebert, B\"ockstedt-Svane and Kreck-Stolz-Teichner. We present the computation of SKK groups for stable tangential structures. Then we consider non-stable examples: the 2-dimensional framed and -spin SKK groups and compute them explicitly using the combinatorial model of framed and -spin surfaces of Novak, Runkel and the author.
Keywords
Cite
@article{arxiv.1907.09428,
title = {On invertible 2-dimensional framed and $r$-spin topological field theories},
author = {Lóránt Szegedy},
journal= {arXiv preprint arXiv:1907.09428},
year = {2022}
}
Comments
24 pages, added references, restructured section 2, added appendix with proofs; final version to be published in Homology, Homotopy and Applications