Seminar of Algebra

Back to main page.

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

Norio Iwase (Kyushu University)
Departamento de Álgebra
Wed, 15 feb 2017 11:30
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.