Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 074, 44 pages      arXiv:2306.07216      https://doi.org/10.3842/SIGMA.2025.074

Cyclic Objects from Surfaces

Ivan Bartulović
Institut für Geometrie, Zellescher Weg 12-14, 01062 Dresden, Germany

Received May 27, 2024, in final form August 20, 2025; Published online September 06, 2025

Abstract
In this paper, we endow the family of all closed genus $g \ge 1$ surfaces 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.

Key words: cyclic objects; cobordisms; topological quantum field theories (TQFTs).

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