On invertible 2-dimensional framed and <i>r</i>-spin topological field theories

Autor(en)

Lorant Szegedy

Abstrakt

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.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Universität Wien

Journal

Homology, Homotopy and Applications

Band

25

Seiten

105-126

Anzahl der Seiten

22

ISSN

1532-0073

DOI

https://doi.org/10.4310/HHA.2023.v25.n1.a6

Publikationsdatum

2023

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Mathematics (miscellaneous)

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/acadd2cf-cc53-414a-b241-bcc380e7e71a