UNITARY FUNCTOR CALCULUS WITH REALITY

Functor Calculus and Operads

Speaker: Gregory Arone (Virginia) Title: Part 1: operads, modules and the chain rule Abstract: Let F be a homotopy functor between the categories of pointed topological spaces or spectra. By the work of Goodwillie, the derivatives of F form a symmetric sequence of spectra ∂∗F . This symmetric sequence determines the homogeneous layers in the Taylor tower of F , but not the extensions in the tow...

Pregroup Calculus as a Logic Functor

Functor Calculus for under Categories and the De Rham Complex

Goodwillie’s calculus of homotopy functors associates a tower of polynomial approximations, the Taylor tower, to a functor of topological spaces over a fixed space. We define a new tower, the varying center tower, for functors of categories with a fixed initial object, such as algebras under a fixed ring spectrum. We construct this new tower using elements of the Taylor tower constructions of B...

Functor Calculus and Operads March 13 – March 18 , 2011 MEALS

Speaker: Gregory Arone (Virginia) Title: Part 1: operads, modules and the chain rule Abstract: Let F be a homotopy functor between the categories of pointed topological spaces or spectra. By the work of Goodwillie, the derivatives of F form a symmetric sequence of spectra ∂∗F . This symmetric sequence determines the homogeneous layers in the Taylor tower of F , but not the extensions in the tow...

The J Functor and the Nonstable Homotopy Groups of the Unitary Groups

The recent work of Adams, Atiyah, Todd, and Walker on the complex Stiefel manifolds has certain implications regarding the structure of the nonstable homotopy groupsir¡(Um),i>2m. The purpose of this note is to set up some of the machinery for investigating these implications. The information we have obtained so far concerning w^Um), i>2m, is contained in Corollary I, stated below. It is likely ...