Unitary functor calculus with reality

Niall Taggart

doi:10.1017/s0017089521000033

Unitary functor calculus with reality

Niall Taggart

School of Mathematics and Physics

Research output: Contribution to journal › Article › peer-review

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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,
BUR(−). The calculus produces a Taylor tower, the n-th layer of which is classified by a
spectrum with an action of C2 U(n). We further give model categorical considerations,
producing a zigzag of Quillen equivalences between spectra with an action of C2 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
Pages (from-to)	197–230
Number of pages	34
Journal	Glasgow Mathematical Journal
Volume	64
DOIs	https://doi.org/10.1017/s0017089521000033
Publication status	Published - 10 Mar 2021

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10.1017/s0017089521000033Licence: CC BY

Unality funtor calculus with reality
© 2021 The Authors. This is an open access article published under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
Final published version, 337 KBLicence: CC BY

Cite this

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title = "Unitary functor calculus with reality",

abstract = "We construct a calculus of functors in the spirit of orthogonal calculus, which is designed to study {\textquoteleft}functors with reality{\textquoteright} such as the Real classifying space functor, BUR(−). The calculus produces a Taylor tower, the n-th layer of which is classified by a spectrum with an action of C2 U(n). We further give model categorical considerations, producing a zigzag of Quillen equivalences between spectra with an action of C2 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.",

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AB - 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, BUR(−). The calculus produces a Taylor tower, the n-th layer of which is classified by a spectrum with an action of C2 U(n). We further give model categorical considerations, producing a zigzag of Quillen equivalences between spectra with an action of C2 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.

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Unitary functor calculus with reality

Abstract

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