Bonn Topology Group - Abstracts

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Talk

November 14, 2023
Christian Carrick (Universiteit Utrecht): Chromatic defect, Wood's theorem, and higher real K-theories

Abstract

Let X(n) be Ravenel's Thom spectrum over \Omega SU(n). We say a spectrum E has chromatic defect n if n is the smallest positive integer such that E\otimes X(n) is complex orientable. We will look closely at this quantity in three cases: when E is a finite spectrum, when E is the fixed points of Morava E-theory with respect to a finite subgroup of the Morava stabilizer group, and when E is an fp spectrum in the sense of Mahowald—Rezk. In this last case, we show that the property of having finite chromatic defect is closely related to the existence of splittings similar to Wood's theorem on ko. When E admits such a splitting, we show that there is a Z-indexed version of ANSS(E) which behaves much like a Tate spectral sequence, and we explore this in detail for E=ko.