One-dimensional topological theories with defects and linear generating functions

Im, Mee Seong; Zimmer, Paul

doi:10.2140/involve.2022.15.319

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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

DOI: 10.2140/involve.2022.15.319

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

Vol. 15, No. 2, 2022