English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We prove that smooth 1-dimensional topological field theories over a manifoldare equivalent to vector bundles with connection. The main novelty is ourdefinition of the smooth 1-dimensional bordism category, which encodes cuttinglaws rather than gluing laws. We make this idea precise through a smoothversion of Rezk's complete Segal spaces. With such a definition in hand, weanalyze the category of field theories using a combination of descent, a smoothversion of the 1-dimensional cobordism hypothesis, and standarddifferential-geometric arguments.

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