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Adjoints and orthogonal groups

Banff International Research Station for Mathematical Innovation and Discovery

In this talk I will articulate and contextualize the following sequence of results. <ul> <li>The Bruhat decomposition of the general linear group defines a stratification of the orthogonal group.</li> <li>Matrix multiplication defines an algebra structure on its exit-path category in a certain Morita category of categories.</li> <li>In this Morita category, this algebra acts on the category of $n$-categories -- this action is given by adjoining adjoints to $n$-categories.</li> </ul> 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; Algebraic topology; Category theory; homological algebra

video/mp4

Author affiliation: Montana State University

2019-03-25

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69190

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/