Invariants of r-spin TQFTs and non-semisimplicity

Autor(en)

Nils Carqueville, Ehud Meir, Lóránt Szegedy

Abstrakt

For a positive integer r, an r-spin topological quantum field theory is a 2-dimensional TQFT with tangential structure given by the r-fold cover of SO2. In particular, such a TQFT assigns a scalar invariant to every closed r-spin surface Σ. Given a sequence of scalars indexed by the set of diffeomorphism classes of all such Σ, we construct a symmetric monoidal category C and a C-valued r-spin TQFT which reproduces the given sequence. We also determine when such a sequence arises from a TQFT valued in an abelian category with finite-dimensional Hom spaces. In particular, we construct TQFTs with values in super vector spaces that can distinguish all diffeomorphism classes of r-spin surfaces, and we show that the Frobenius algebras associated to such TQFTs are necessarily non-semisimple.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

University of Aberdeen, Universität Wien

Journal

Journal of Algebra

Band

664/Part A

Seiten

101-128

Anzahl der Seiten

28

ISSN

0021-8693

DOI

https://doi.org/10.48550/arXiv.2306.08608

Publikationsdatum

02-2025

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Algebra and Number Theory

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/3a398d5f-80c2-42b0-9e28-be5525c233a1