Home > Proceedings > Adv. Stud. Pure Math. > Primitive Forms and Related Subjects — Kavli IPMU 2014 > TQFT, homological algebra and elements of K. Saito's theory of Primitive form: an attempt of mathematical text written by mathematical physicist
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VOL. 83 | 2019 TQFT, homological algebra and elements of K. Saito's theory of Primitive form: an attempt of mathematical text written by mathematical physicist
Andrey Losev

Editor(s) Kentaro Hori, Changzheng Li, Si Li, Kyoji Saito

Abstract

The text is devoted to explanation of the concept of Topological Quantum Field Theory (TQFT), its application to homological algebra and to the relation with the theory of good section from K. Saito's theory of Primitive forms. TQFT is explained in Dirac-Segal framework, 1 dimensional examples are explained in detail. As a first application we show how it can be used in explicit construction of reduction of $\infty$-structure after contraction of a subcomplex. Then we explain Associativity and Commutativity equations using this language. We use these results to construct solutions to Commutativity equations and find a new proof of for the fact that tree level BCOV theory solved Oriented Associativity equations.

Information

Published: 1 January 2019
First available in Project Euclid: 26 December 2019

zbMATH: 07276144

Digital Object Identifier: 10.2969/aspm/08310269

Subjects:
Primary: 18G99, 81T45