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

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

摘要

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

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.

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