Unitary Functor Calculus with Reality

Niall Taggart

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arXiv · 2004.14886

Unitary Functor Calculus with Reality

Niall Taggart

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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.

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BibTeX RIS

Niall Taggart. 2020-04-30. Unitary Functor Calculus with Reality. https://arxiv.org/abs/2004.14886

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