STRUCTURE TO POLYNOMIAL FUNCTORS IN ORTHOGONAL CALCULUS II

  • L. Osei Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi,
  • W. Obeng-Denteh Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi,
  • I. Owusu-Mensah Faculty of Science Education, Akenten Appiah-Menkah University of Skilled Training and Entrepreneurial Development, Mampong-Ashanti,
  • D.D. Zigli Department of Mathematical Sciences, University of Mines and Technology, Tarkwa,

Abstract

The orthogonal calculus of functors is a beautiful tool for calculating the homotopical properties of functors from the category of inner product spaces to pointed spaces or any space enriched over . 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 .This structure is considered in this study

Published
2021-10-17
Section
ARTICLES