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arXiv · 1501.00967

Smooth one-dimensional topological field theories are vector bundles with connection

Daniel Berwick-Evans·Dmitri Pavlov
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Abstract

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.

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BibTeXRIS

Daniel Berwick-Evans, Dmitri Pavlov. 2015-01-05. Smooth one-dimensional topological field theories are vector bundles with connection. https://doi.org/10.2140/agt.2023.23.3707

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