Abstract
We construct a calculus of functors in the spirit of orthogonal calculus, which is designed to study "functors with reality" such as the Real classifying space functor, $BU_\mathbb{R}()$. The calculus produces a Taylor tower, the $n$th layer of which is classified by a spectrum with an action of $C_2 \ltimes U(n)$. We further give model categorical considerations, producing a zigzag of Quillen equivalences between spectra with an action of $C_2 \ltimes U(n)$ and a model structure on the category of input functors which captures the homotopy theory of the $n$th layer of the Taylor tower.
Original language  English 

Type  Online preprint 
Media of output  ArXiv preprint server 
Publication status  Published  30 Apr 2020 
Bibliographical note
27 pagesKeywords
 math.AT
 55P65 (Primary) 55P42, 55P91, 55U35 (Secondary)
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Dive into the research topics of 'Unitary Functor Calculus with Reality'. Together they form a unique fingerprint.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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