Vol. 15, No. 2, 2022

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One-dimensional topological theories with defects and linear generating functions

Mee Seong Im and Paul Zimmer

Vol. 15 (2022), No. 2, 319–331
Abstract

We study the Gram determinant and construct bases of hom spaces for the one-dimensional topological theory of decorated unoriented one-dimensional cobordisms, as recently defined by Khovanov, when the pair of generating functions is linear.

Keywords
topological quantum field theory, cobordism, universal construction, string diagrams, defects, evaluations, linear generating functions
Mathematical Subject Classification
Primary: 18M30
Secondary: 05A15, 57K16
Milestones
Received: 19 May 2021
Accepted: 16 September 2021
Published: 29 July 2022

Communicated by Józef H. Przytycki
Authors
Mee Seong Im
Department of Mathematics
United States Naval Academy
Annapolis, MD
United States
Paul Zimmer
Department of Mathematics
United States Naval Academy
Annapolis, MD
United States