Defining extended TQFTs via handle attachments
Geometric Topology
2026-01-13 v2 Category Theory
Quantum Algebra
Abstract
We give a finite presentation of the cobordism symmetric monoidal bicategory of (smooth, oriented) closed manifolds, cobordisms and cobordisms with corners as an extension of the bicategory of closed manifolds, cobordisms and diffeomorphisms. The generators are the standard handle attachments, and the relations are handle cancellations and invariance under reversing the orientation of the attaching spheres. In other words, given a categorified TQFT and 2-morphisms associated to the standard handles satisfying our relations, we construct a once extended TQFT.
Cite
@article{arxiv.2412.14649,
title = {Defining extended TQFTs via handle attachments},
author = {Benjamin Haïoun},
journal= {arXiv preprint arXiv:2412.14649},
year = {2026}
}
Comments
v2: Many figures added. To appear in Algebraic and Geometric Topology. Comments welcome!