2020/04/30 by Niall Taggart, Taggart, Niall
Mathematics · #55P65 (Primary) 55P42 #55P91 #55U35 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:55P42 #msc:55P65 #msc:55P91 #msc:55U35
paper · pdf · doi:10.48550/arxiv.2004.14886
27 pages, v.2 accepted version
arxiv created 2021/11/22 · arxiv updated 2021/11/23
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_ℝ(-). The calculus produces a Taylor tower, the n-th layer of which is classified by a spectrum with an action of C2 \ltimes U(n). We further give model categorical considerations, producing a zig-zag of Quillen equivalences between spectra with an action of C2 \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.