The topological modular forms of RP2 and RP2 ∧ CP2

Beaudry, Agnès; Bobkova, Irina; Pham, Viet-Cuong; Xu, Zhouli

doi:10.1112/topo.12263

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Journal Article

The topological modular forms of RP² and RP² ∧ CP²

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Pham, Viet-Cuong
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1112/topo.12263
(Publisher version)

https://doi.org/10.48550/arXiv.2103.10953
(Preprint)

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Citation

Beaudry, A., Bobkova, I., Pham, V.-C., & Xu, Z. (2022). The topological modular forms of RP² and RP² ∧ CP². Journal of Topology, 15(4), 1864-1926. doi:10.1112/topo.12263.

Cite as: https://hdl.handle.net/21.11116/0000-000B-3789-D

Abstract

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