Unitary Functor Calculus with Reality

Niall Taggart

Research output: Other contribution

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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 zig-zag 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 languageEnglish
TypeOnline preprint
Media of outputArXiv preprint server
Publication statusPublished - 30 Apr 2020

Bibliographical note

27 pages

Keywords

  • math.AT
  • 55P65 (Primary) 55P42, 55P91, 55U35 (Secondary)

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