The topological modular forms of RP2$\mathbb {R}P^2$ and RP2∧CP2$\mathbb {R}P^2 \wedge \mathbb {C}P^2$. Issue 4 (19th September 2022)

• Record Type: Journal Article
• Authors: Beaudry, Agnès; Bobkova, Irina; Pham, Viet‐Cuong; Xu, Zhouli
• Is Part Of: Journal of topology. Volume 15:Issue 4(2022)
• Page Start: 1864
• Page End: 1926
• Publication Date: 2022-09-19
• Subjects: Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12263
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract: We study the elliptic spectral sequence computing t m f ∗ ( R P 2 ) $tmf_*(\mathbb {R}P^2)$ and t m f ∗ ( R P 2 ∧ C P 2 ) $tmf_* (\mathbb {R} P^2 \wedge \mathbb {C} P^2)$ . Specifically, we compute all differentials and resolve exotic extensions by 2, η $\eta$, and ν $\nu$ . For t m f ∗ ( R P 2 ∧ C P 2 ) $tmf_* (\mathbb {R} P^2 \wedge \mathbb {C} P^2)$, we also compute the effect of the v 1 $v_1$ ‐self maps of R P 2 ∧ C P 2 $\mathbb {R} P^2 \wedge \mathbb {C} P^2$ on t m f $tmf$ ‐homology.