Higher chromatic analogues of twisted $K$theory
M. Khorami
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 Jhomomorphism. We investigate some of the properties of these new twisted theories and discuss why we consider them
as a generalization of twisted Ktheory to higher chromatic levels.
Tbilisi Mathematical Journal, Vol. 12(2) (2019), pp. 153162
