TL;DR
This paper explores the use of cochains to analyze 2- and 3-dimensional topological quantum field theories, establishing new algebraic structures and properties inspired by Baez's categorical framework.
Contribution
It introduces cochains as a tool to study 2- and 3-TQFTs and proves they form an $A_{ olinebreak}_{ olinebreak}infty$ algebra under specific conditions.
Findings
Cochains satisfy certain properties in 2- and 3-TQFTs.
Under specific conditions, cochains form an $A_{ olinebreak}_{ olinebreak}infty$ algebra.
Provides algebraic insights into topological quantum field theories.
Abstract
John C.Baez reinterpreted 2-dimensional and 3-dimensional topological quantum field theories (abbreviated as 2-TQFT and 3-TQFT) in "A prehistory of n-categorical physics"[JC11]. Inspired by his idea, this paper utilizes cochains to prove some properties of 2-TQFT and 3-TQFT. We also prove that cochains form an algebra under certain conditions.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology