Open Collections

Description

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 category 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.