Cyclic Objects from Surfaces

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• Main Author: Bartulović, Ivan
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/214172
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Cyclic Objects from Surfaces. Ivan Bartulović. SIGMA 21 (2025), 074, 44 pages

In this paper, we endow the family of all closed genus ≥ 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.