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

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

doi:10.1112/topo.12263

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

Algebraic Topology 2023-01-30 v2

Authors: Agnès Beaudry , Irina Bobkova , Viet-Cuong Pham , Zhouli Xu

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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.

Keywords

topological modular forms elliptic spectral sequence differentials exotic extensions tmf-homology self maps

Cite

@article{arxiv.2103.10953,
  title  = {The topological modular forms of $\mathbb{R}P^2$ and $\mathbb{R}P^2 \wedge \mathbb{C}P^2$},
  author = {Agnès Beaudry and Irina Bobkova and Viet-Cuong Pham and Zhouli Xu},
  journal= {arXiv preprint arXiv:2103.10953},
  year   = {2023}
}

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

Abstract

Keywords

Cite

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