Smooth one-dimensional topological field theories are vector bundles with connection Article Swipe
Related Concepts
Mathematics
Connection (principal bundle)
Vector bundle
Topology (electrical circuits)
Field (mathematics)
Vector field
Pure mathematics
Geometry
Combinatorics
Daniel Berwick-Evans
,
Dmitri Pavlov
·
YOU?
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· 2023
· Open Access
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· DOI: https://doi.org/10.2140/agt.2023.23.3707
· OA: W121250879
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.2140/agt.2023.23.3707
· OA: W121250879
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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