PreprintarXiv licencearXiv
Involutions on (∞,n)-categories of bordisms and reflection TQFTs
Abstract
We construct a strict involution, that is, a strict ℤ/2-action, on the (∞,n)-category Bordn(Hn) of bordisms with Hn-structure, where Hn is the symmetry type of a TQFT, using the complete n-fold Segal space model. Using this involution, we develop an appropriate definition of reflection TQFTs in this setting and show that they correspond to certain homotopy fixed point spaces. Finally, we apply the machinery to the example of super algebras, where, depending on the symmetry type, the homotopy fixed point data corresponds to either a stellar structure or a real structure on the algebra that the reflection theory assigns to the point.
Related
- Unitary TQFTs, unitary disk-like n-categories, and higher Hilbert spaces
- Equivalence of categories of bivariant K-theory for C*-algebras over topological spaces via reflection functors
- Reduced characteristic number criteria for Tk- and (ℤ2)k-equivariant bordisms
- Defect TQFTs, the Generalized Cobordism Hypothesis, and Algebraic K-Theory
- On the Relation Between Non-Semisimple TQFTs
BibTeX
@misc{brunialti2026involutions,
title = {{Involutions on $(\infty,n)$-categories of bordisms and reflection TQFTs}},
author = {Pedro Brunialti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23712},
eprint = {2610.23712},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23712},
}
RIS
TY - UNPB
TI - Involutions on (∞,n)-categories of bordisms and reflection TQFTs
AU - Pedro Brunialti
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23712
UR - https://arxiv.org/abs/2610.23712
AB - We construct a strict involution, that is, a strict ℤ/2-action, on the (∞,n)-category Bord_n(H_n) of bordisms with H_n-structure, where H_n is the symmetry type of a TQFT, using the complete n-fold Segal space model. Using this involution, we develop an appropriate definition of reflection TQFTs in this setting and show that they correspond to certain homotopy fixed point spaces. Finally, we apply the machinery to the example of super algebras, where, depending on the symmetry type, the homotopy fixed point data corresponds to either a stellar structure or a real structure on the algebra that the reflection theory assigns to the point.
ER -