# Homotopy theory of $A_n$-spaces in Lie groups

Date:

2019/06/26 Wed 16:30 - 17:30

Room:

Room 110, Building No.3

Speaker:

Mitsunobu Tsutaya

Affiliation:

Kyushu University

Abstract:

An $A_n$-space is a topological space equipped with a continuous unital binary operation satisfying certain higher homotopy associativity conditions depending on $n=1,2,\ldots,\infty$. Similarly, we can also define several versions of higher homotopy commutativities of $A_n$-spaces. Lie groups are basic examples of $A_\infty$-spaces. The speaker has been working on problems in homotopy theory of $A_n$-spaces in Lie groups.

In this talk, we will review the basics of higher homotopy associativity and commutativity and the results in Lie groups especially related to higher homotopy commutativity.