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

Pub Date : 2022-09-19 DOI:10.1112/topo.12263

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

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引用次数: 1

Abstract

We study the elliptic spectral sequence computing $t m f_{*} (R P^{2})$ and $t m f_{*} (R P^{2} \land C P^{2})$ . Specifically, we compute all differentials and resolve exotic extensions by 2, $η$ , and $ν$ . For $t m f_{*} (R P^{2} \land C P^{2})$ , we also compute the effect of the $v_{1}$ -self maps of $R P^{2} \land C P^{2}$ on $t m f$ -homology.

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rp2 $\mathbb {R}P^2$和rp2∧cp2 $\mathbb {R}P^2 \wedge \mathbb {C}P^2$的拓扑模形式

研究了椭圆谱序列计算tmf∗(R p2)$ tmf_*(\mathbb {R}P^2)$和tmf * (rp2∧cp2) $tmf_* (\mathbb {R} P^2 \wedge\mathbb {C} P^2)$。具体来说，我们计算了所有的微分，并通过2，η $\eta$和ν $\nu$来解析奇异的扩展。对于t m f * (rp2∧cp2)$tmf_* (\mathbb {R} P^2 \wedge \mathbb {C} P^2)$，我们还计算了rp2∧cp2 $\mathbb {R} P^2 \wedge \mathbb {C} P^2$的v1 $v_1$ -自映射的作用T mf$ tmf$ -同源性。

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