Abstract
We construct the unitary analogue of orthogonal calculus developed by Weiss, utilising model categories to give a clear description of the intricacies in the equivariance and homotopy theory involved. The subtle differences between real and complex geometry lead to subtle differences between orthogonal and unitary calculus. To address these differences we construct unitary spectra - a variation of orthogonal spectra - as a model for the stable homotopy category. We show through a zig-zag of Quillen equivalences that unitary spectra with an action of the $n$-th unitary group models the homogeneous part of unitary calculus. We address the issue of convergence of the Taylor tower by introducing weakly polynomial functors, which are similar to weakly analytic functors of Goodwillie but more computationally tractable.
Original language | English |
---|---|
Type | Online preprint |
Media of output | ArXiv preprint server |
Publication status | Submitted - 19 Nov 2019 |
Publication series
Name | arXiv |
---|
Bibliographical note
30 pagesKeywords
- Homotopy theory
- functor calculus
- stable homotopy theory
- equivariant homotopy theory
ASJC Scopus subject areas
- Geometry and Topology
Fingerprint
Dive into the research topics of 'Unitary calculus: model categories and convergence'. Together they form a unique fingerprint.Student Theses
-
Beyond orthogonal calculus: The unitary and real cases
Author: Taggart, N., Dec 2020Supervisor: Todorov, I. (Supervisor), Barnes, D. (Supervisor) & McFetridge, L. (Supervisor)
Student thesis: Doctoral Thesis › Doctor of Philosophy
File