CP(V) 的有理圆变椭圆同调

IF 0.8 4区数学 Q2 MATHEMATICS

Homology Homotopy and Applications Pub Date : 2024-09-18 DOI:10.4310/hha.2024.v26.n2.a3

Matteo Barucco

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引用次数: 0

摘要

$def\T\{mathbb{T}}\def\CPV{\mathbb{C}P(V)}$ 我们证明了理性 $\T^2$- 和 $\T$-equivariant elliptic cohomology 的代数模型之间的分裂结果，其中 $\T$ 是圆组，$\T^2$ 是 2$-torus。作为应用，我们计算了$\CPV$的有理$\T$-后向椭圆同调：有限维复数$\T$-表示$V$的复线的$\T$-空间。这是通过将 $\CPV$ 的 $\T$-elliptic cohomology 计算简化为计算复数表示的某些球的 $\T^2$-elliptic cohomology 来实现的。

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Rational circle-equivariant elliptic cohomology of CP(V)

$\def\T{\mathbb{T}}\def\CPV{\mathbb{C}P(V)}$ We prove a splitting result between the algebraic models for rational $\T^2$- and $\T$-equivariant elliptic cohomology, where $\T$ is the circle group and $\T^2$ is the $2$-torus. As an application we compute rational $\T$-equivariant elliptic cohomology of $\CPV$: the $\T$-space of complex lines for a finite dimensional complex $\T$-representation $V$. This is achieved by reducing the computation of $\T$-elliptic cohomology of $\CPV$ to the computation of $\T^2$-elliptic cohomology of certain spheres of complex representations.

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来源期刊

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.