A faithful 2-dimensional TQFT
Stevan Gajovic, Zoran Petric, Sonja Telebakovic
TL;DR
This paper demonstrates that a specific commutative Frobenius algebra provides a complete and faithful invariant for two-dimensional cobordisms, establishing a rigorous link between algebraic structures and 2D quantum field theories.
Contribution
It introduces a particular algebraic invariant that fully characterizes 2D cobordisms, utilizing Zsigmondy's Theorem in the proof.
Findings
The algebraic invariant is complete for 2D cobordisms.
The quantum field theory constructed is faithful.
Zsigmondy's Theorem is essential in the proof.
Abstract
It has been shown in this paper that the commutative Frobenius algebra provides a complete invariant for two-dimensional cobordisms, i.e., that the corresponding two-dimensional quantum field theory is faithful. The essential role in the proof of this result plays Zsigmondy's Theorem.
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