CATS3

Derived smooth manifolds

speaker: David Spivak (University of Oregon)

abstract: A derived manifold is a space with a homotopical sheaf of C^\infty rings, which locally looks like the zero set of smooth functions on a manifold.

I will give an axiomatization of derived manifolds, which is designed to allow one to understand their behavior without being immersed in the technical details. From these axioms, I will show that the cobordism theory of derived manifolds is equivalent to that of smooth manifolds, and that in particular, every derived manifold has a fundamental cobordism class. In particular, a cup product formula of the form

A\cap B = A \cup B,

for derived submanifolds A and B, holds with full generality.

timetable:
Wed 3 Sep, 14:30 - 15:30, Aula Bianchi Scienze
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