Cyclic objects from surfaces
Abstract
In this paper, we endow the family of closed oriented genus $g$ surfaces, starting with torus, with a structure of a (co)cyclic object in the category of $3$-dimensional cobordisms. As a corollary, any $3$-dimensional TQFT induces a (co)cyclic module, which we compute algebraically for the Reshetikhin-Turaev TQFT.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2023
- DOI:
- arXiv:
- arXiv:2306.07216
- Bibcode:
- 2023arXiv230607216B
- Keywords:
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- Mathematics - Geometric Topology;
- Mathematics - Quantum Algebra;
- 2020 Mathematics Subject Classification. 18N50;
- 57K16
- E-Print:
- 48 pages, many figures. Minor changes done. Comments are still welcome!