Geodesic
Smooth one-dimensional topological field theories are vector bundles with connection
Berwick-Evans, Daniel1 ; Pavlov, Dmitri2
1 Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, United States
2 Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, United States
Algebraic and Geometric Topology, Tome 23 (2023) no. 8, pp. 3707-3743

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We prove that smooth 1–dimensional topological field theories over a manifold are equivalent to vector bundles with connection. The main novelty is our definition of the smooth 1–dimensional bordism category, which encodes cutting laws rather than gluing laws. We make this idea precise through a smooth version of Rezk’s complete Segal spaces. With such a definition in hand, we analyze the category of field theories using a combination of descent, a smooth version of the 1–dimensional cobordism hypothesis, and standard differential-geometric arguments.

DOI : 10.2140/agt.2023.23.3707
Keywords: functorial field theory

Berwick-Evans, Daniel 1 ; Pavlov, Dmitri 2

1 Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, United States
2 Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, United States 
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Berwick-Evans, Daniel; Pavlov, Dmitri. Smooth one-dimensional topological field theories are vector bundles with connection. Algebraic and Geometric Topology, Tome 23 (2023) no. 8, pp. 3707-3743. doi: 10.2140/agt.2023.23.3707

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