The topological modular forms of $\mathbb{R}{P}^2$ and $\mathbb{R}{P}^2\wedge \mathbb{C}{P}^2$

Abstract

In this paper, we study the elliptic spectral sequence computing $tm{f}_{\ast }(\mathbb{R}{P}^2)$ and $tm{f}_{\ast }(\mathbb{R}{P}^2\wedge \mathbb{C}{P}^2)$. Specifically, we compute all differentials and resolve exotic extensions by 2, $\eta$, and $\nu$. For $tm{f}_{\ast }(\mathbb{R}{P}^2\wedge \mathbb{C}{P}^2)$, we also compute the effect of the $v_1$-self maps of $\mathbb{R}{P}^2\wedge \mathbb{C}{P}^2$ on $tmf$-homology.

Cited by in corpus (2)

• Bordism for the 2-group symmetries of the heterotic and CHL strings
• The localization of orthogonal calculus with respect to homology