Fully extended r-spin TQFTs

Autor(en)

Nils Carqueville, Lorant Szegedy

Abstrakt

We prove the r-spin cobordism hypothesis in the setting of (weak) 2-categories for every positive integer r: The 2-groupoid of 2-dimensional fully extended r-spin TQFTs with given target is equivalent to the homotopy fixed points of an induced Spinr 2-action. In particular, such TQFTs are classified by fully dualisable objects together with a trivialisation of the rth power of their Serre automorphisms. For r = 1, we recover the oriented case (on which our proof builds), while ordinary spin structures correspond to r = 2. To construct examples, we explicitly describe Spinr 2-homotopy fixed points in the equivariant completion of any symmetric monoidal 2-category. We also show that every object in a 2-category of Landau–Ginzburg models gives rise to fully extended spin TQFTs and that half of these do not factor through the oriented bordism 2-category.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

IST Austria - Institute of Science and Technology

Journal

Quantum Topology

Band

14

Seiten

467–532

Anzahl der Seiten

66

DOI

https://doi.org/10.4171/QT/193

Publikationsdatum

07-2021

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Geometry and Topology, Mathematical Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/466351aa-8824-42b0-af64-6a732deffb81