# Seminar of Algebra

### Co-category and co-$A_{\infty}$ structure

Speaker:
Norio Iwase (Kyushu University)
Email:
iwase@math.kyushu-u.ac.jp
Location:
Departamento de Álgebra
Date:
Wed, 15 feb 2017 11:30
Bio:
Prof. Iwase is interested in Algebraic Topology, mainly on $A_{\infty}$ structures, Lusternik-Schnirelmann category of a space and their duals in unstable homotopy category.

This is an on-going project and the story goes like that.  We know several different approaches to introduce co-categories of a space, which could not apparently be the same.  These notions are closely related to the desuspension problem of a suspended space.  In this talk, we show how we are trying to use the co-$A_\infty$ structure of a suspension space to desuspend.  At this moment, we are facing a problem in a process to connect to the Mike Hopkins co-category, which is caused by the existence of a homotopy unit, and so we are led to use a version of Muro-Tonks unital associahedra.