Abstract
The orthogonal and unitary calculi give a method to study functors from the category of real or complex inner product spaces to the category of based topological spaces. We construct functors between the calculi from the complexificationrealification adjunction between real and complex inner product spaces. These allow for movement between the versions of calculi, and comparisons between the Taylor towers produced by both calculi. We show that when the inputted orthogonal functor is weakly polynomial, the Taylor tower of the functor restricted through realification and the restricted Taylor tower of the functor agree up to weak equivalence. We further lift the homotopy level comparison of the towers to a commutative diagram of Quillen functors relating the model categories for orthogonal calculus and the model categories for unitary calculus.
Original language  English 

Type  Online preprint 
Media of output  ArXiv preprint server 
Publication status  Submitted  13 Jan 2020 
Publication series
Name  arXiv 

Keywords
 Functor Calculus
 Stable homotopy theory
 equivariant homotopy theory
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Student Theses

Beyond orthogonal calculus: The unitary and Real cases
Author: Taggart, N., Dec 2020Supervisor: Todorov, I. (Supervisor), Barnes, D. (Supervisor) & McFetridge, L. (Supervisor)
Student thesis: Doctoral Thesis › Doctor of Philosophy
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