A note on the (∞,n)–category of cobordisms

By Damien Calaque, Claudia I. Scheimbauer. Algebraic and Geometric Topology, 2015

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In this note we give a precise definition of fully extended topological field theories a la Lurie. Using complete n-fold Segal spaces as a model, we construct an $(\infty,n)$-category of $n$-dimensional cobordisms, possibly with tangential structure. We endow it with a symmetric monoidal structure and show that we can recover the usual category of cobordisms and the cobordism bicategory from it.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/30c1426ebec829f42be3bfb40021123abab6e253