Orthogonal group and higher categorical adjoints

Abstract: In this talk I will articulate and contextualize the following sequence of results.

* The Bruhat decomposition of the general linear group defines a stratification of the orthogonal group.

* Matrix multiplication defines an algebra structure on its exit-path category in a certain Morita category of categories.

* In this Morita category, this algebra acts on the categeory of n-categories -- this action is given by adjoining adjoints to n-categories.

This result is extracted from a larger program -- entirely joint with John Francis, some parts joint with Nick Rozenblyum -- which proves the cobordism hypothesis.

Mathematics

Audience: researchers in the discipline

Caltech geometry/topology seminar