The $E_2^{h{C}_6}$-homology of $\mathbb{R}{P}^2$ and $\mathbb{R}{P}^2\wedge \mathbb{C}{P}^2$

Abstract

Let $E_2$ be the Morava E-theory of height 2 at the prime 2. In this paper, we compute the homotopy groups of $E_2^{h{C}_6}\wedge \mathbb{R}{P}^2$ and $E_2^{h{C}_6}\wedge \mathbb{R}{P}^2\wedge \mathbb{C}{P}^2$ using the homotopy fixed point spectral sequences.

17 pages, 14 figures