2025/01/23 by Yavuz, Emel
Computer Science · Engineering · Mathematics · #55P42 #55P91 #55U35 #Advanced Numerical Analysis Techniques #Algebraic Topology (math.AT) #FOS: Mathematics #Mathematics and Applications #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2501.14077
openalex publication_date 2025/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we construct a version of orthogonal calculus for functors from C2-representations to C2-spaces, where C2 is the cyclic group of order 2. For example, the functor BO(-), that sends a C2-representation to the classifying space of its orthogonal group, which has a C2-action induced by the action on the C2-representation. We obtain a bigraded sequence of approximations to such a functor, and via a zig-zag of Quillen equivalences, we prove that the homotopy fibres of maps between approximations are fully determined by orthogonal spectra with a genuine action of C2 and a naive action of the orthogonal group O(p,q):=O(ℝp+qδ).