Geodesic
On invertible $2$-dimensional framed and $r$-spin topological field theories
Homology, homotopy, and applications, Tome 25 (2023) no. 1, pp. 105-126.

Voir la notice de l'article provenant de la source International Press of Boston

We classify invertible $2$-dimensional framed and $r$-spin topological field theories by computing the homotopy groups and the $k$-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, Bökstedt–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 $r$-spin SKK groups and compute them explicitly using the combinatorial model of framed and $r$-spin surfaces of Novak, Runkel and the author.
DOI : 10.4310/HHA.2023.v25.n1.a6
Classification : 57R15, 57R56
Keywords: invertible topological field theory, spin, SKK group, bordism group 
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Lóránt Szegedy. On invertible $2$-dimensional framed and $r$-spin topological field theories. Homology, homotopy, and applications, Tome 25 (2023) no. 1, pp. 105-126. doi : 10.4310/HHA.2023.v25.n1.a6. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n1.a6/

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