Abstract
We construct the unitary analogue of orthogonal calculus developed by Weiss, utilising model categories to give a clear description of the intricacies in the equivariance and homotopy theory involved. The subtle differences between real and complex geometry lead to subtle differences between orthogonal and unitary calculus. To address these differences we construct unitary spectra  a variation of orthogonal spectra  as a model for the stable homotopy category. We show through a zigzag of Quillen equivalences that unitary spectra with an action of the $n$th unitary group models the homogeneous part of unitary calculus. We address the issue of convergence of the Taylor tower by introducing weakly polynomial functors, which are similar to weakly analytic functors of Goodwillie but more computationally tractable.
Original language  English 

Type  Online preprint 
Media of output  ArXiv preprint server 
Publication status  Submitted  19 Nov 2019 
Publication series
Name  arXiv 

Bibliographical note
30 pagesKeywords
 Homotopy theory
 functor calculus
 stable homotopy theory
 equivariant homotopy theory
ASJC Scopus subject areas
 Geometry and Topology
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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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