Tilman Bauer: Finite loop spaces and their classification

Consider a space X which has the following two properties:

1. it is equivalent to the based loop space of another space Y, and
2. its homology is trivial above a certain dimension, and finitely generated up to that dimension.

Compact Lie groups are prominent examples of such “finite loop spaces", but they are by no means the only ones. In this talk, I will show how modern methods of homotopy theory can be applied to study finite loop spaces, leading to a very satisfying and surprisingly rigid classification theorem and a source of new, exotic examples of almost-but-not-quite Lie groups.

The talk will be directed to a general audience.