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oai:figshare.com:article/32639820 2026-10-01T16:36:47Z portal_1172 item_type_8 month_year_10_2026

C2-equivariant orthogonal calculus Emel Yavuz (24168894) PUREID: 598463798 Equivariant orthogonal calculus orthogonal calculus functor calculus In this thesis, we construct a new version of orthogonal calculus for functors F from C_2 representations to C_2 spaces, where C_2 is the cyclic group of order 2. For example, the functor BO(-), which sends a C_2 representation V to the classifying space of its orthogonal group BO(V). We obtain a bigraded sequence of approximations to F, called the strongly (p,q)-polynomial approximations T_{p,q}F. The bigrading arises from the bigrading on C_2 representations. The homotopy fibre D_{p,q}F of the map from T_{p+1,q}T_{p,q+1}F to T_{p,q}F is such that the approximation T_{p+1,q}T_{p,q+1}D_{p,q}F is equivalent to the functor D_{p,q}F itself and the approximation T_{p,q}D_{p,q}F is trivial. A functor with these properties is called (p,q)-homogeneous. Via a zig-zag of Quillen equivalences, we prove that (p,q)-homogeneous functors are fully determined by orthogonal spectra with a genuine action of C_2 and a naive action of the orthogonal group O(p,q). <br><br> 2026-10-01T16:36:47Z Text Thesis 10.17034/32639820.v1 https://figshare.com/articles/thesis/C2-equivariant_orthogonal_calculus/32639820 All Rights Reserved