Translator Disclaimer
April 2019 Higher chromatic analogues of twisted $K$-theory
Mehdi Khorami
Tbilisi Math. J. 12(2): 153-162 (April 2019). DOI: 10.32513/tbilisi/1561082574

Abstract

In this paper we introduce a new family of twisted $K(n)$-local homology theories. These theories are given by the spectra $R_n= E_n^{hS\mathbb G_n}$, twisted by a class $H\in H^{n+2}(X, \mathbb Z_p)$. Here $E_n^{hS\mathbb G_n}$ are the homotopy fixed point spectra under the action of the subgroup $S\mathbb G_n$ of the Morava stabilizer group where $S\mathbb G_n$ is the kernel of the determinant homomorphism $\text{det}:\mathbb G_n\to \mathbb Z_p^\times$. These spectra were utilized in [8] by C. Westerland to study higher chromatic analogues of the J-homomorphism. We investigate some of the properties of these new twisted theories and discuss why we consider them as a generalization of twisted $K$-theory to higher chromatic levels.

Citation

Download Citation

Mehdi Khorami. "Higher chromatic analogues of twisted $K$-theory." Tbilisi Math. J. 12 (2) 153 - 162, April 2019. https://doi.org/10.32513/tbilisi/1561082574

Information

Received: 26 November 2018; Accepted: 27 April 2019; Published: April 2019
First available in Project Euclid: 21 June 2019

zbMATH: 07172319
MathSciNet: MR3973266
Digital Object Identifier: 10.32513/tbilisi/1561082574

Subjects:
Primary: 55N20

Rights: Copyright © 2019 Tbilisi Centre for Mathematical Sciences

JOURNAL ARTICLE
10 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.12 • No. 2 • April 2019
Back to Top