Homology, Homotopy and Applications

Volume 22 (2020)

Number 1

A faithful 2-dimensional TQFT

Pages: 391 – 399

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n1.a22


S. Gajović (Bernoulli Institute, University of Groningen, The Netherlands)

Z. Petrić (Mathematical Institute SANU, Belgrade, Serbia)

S. Telebaković Onić (Faculty of Mathematics, University of Belgrade, Serbia)


It has been shown in this paper that the commutative Frobenius algebra $\mathbb{QZ}_5 \otimes Z(\mathbb{QS}_3)$ provides a complete invariant for two-dimensional cobordisms, i.e., that the corresponding two-dimensional quantum field theory is faithful. Zsigmondy’s Theorem is essential to the proof of this result.


Frobenius algebra, topological quantum field theory, faithful functor, Zsigmondy’s Theorem

2010 Mathematics Subject Classification

15A69, 18A22, 18D10, 57R56

This work was supported by projects 174026 and 174032 of the Ministry of Education, Science, and Technological Development of the Republic of Serbia. The first author was supported by DFG-Grant MU 4110/1-1.

Received 13 March 2019

Received revised 25 July 2019

Accepted 9 August 2019

Published 8 January 2020