Structure to polynomial functors in orthogonal calculus II

Abstract

The orthogonal calculus of functors is a beautiful tool for calculatingthe homotopical properties of functors from the category of inner product spaces to pointed spaces or any space enriched over Top_* . It splits a functor F into a Taylor tower of fibrations, where our n-th fibrations will consist of maps from the n-polynomial approximation of F to the (n − 1)− polynomial approximation of F. The homotopy fiber or layer (the difference between n-polynomial and (n − 1)− polynomial approximation) of this map is then an n-homogeneous functor and is classified by an O (n)- spectrum up to homotopy which is usually denoted as  D_nF.This structure is considered in this study.