Delooping the functor calculus tower

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 Join Construction for Free Involutions on Spheres

Given a manifold X , the set of manifold structures on X × ∆ relative to the boundary can be viewed as the k-th homotopy group of a space S̃s(X). This space is called the block structure space of X . Free involutions on spheres are in one-to-one correspondence with manifold structures on real projective spaces. We generalize Wall’s join construction for free involutions on spheres to define a fu...