Applications of Trace Formalism to DG Categories

Student: Salmagambetov Kirill

Supervisor: Andrey S. Losev

Educational Programme: Mathematics (Master)

Year of Graduation: 2018

This paper is devoted to certain applications of the formalism of traces in symmetric monoidal categories to problems in the world of dg categories. We use the functoriality properties of traces in order to give a new proof of the theorem of Goodwille and Jones simplifying the original argument. In order to make $S^{1}$ equivariant transparent we establish a direct connection between trace formalism and one dimensional topological field theory.

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