论文标题
CP（V）的理性圈子等级椭圆
Rational circle-equivariant elliptic cohomology of CP(V)
论文作者
论文摘要
我们计算CP（v）的有理$ T $ - 等级椭圆共同体，其中$ t $是圆组，CP（v）是$ t $ - $ t $空间，用于有限的尺寸复杂$ t $ t $ -precresentation v。从复杂数字和$ ell condecient condection $ ncorivation $ ncorivation-equorivation-equivation n e Ellimit contequiv conterivation，我们可以实现$ the $ the $ the uptimation $ the，我们可以实现$ ncorivation $ exiert $ the，我们的标识是$ eximive，我们计算了计算。 [GRE05]中内置的$ ec_t $ cohomology理论和$ t^2 $ - equivariant椭圆形的共同体学理论$ ec_ {t^2} $内置的[bar22]是1x $ t $ split。该结果使我们能够将$ ec_t（cp（v））$的计算减少到已经在[BAR22]中执行的复杂表示领域的$ t^2 $ elliptic-elliptic-elliptic eliptication。
We compute rational $T$-equivariant elliptic cohomology of CP(V), where $T$ is the circle group, and CP(V) is the $T$-space of complex lines for a finite dimensional complex $T$-representation V. Starting from an elliptic curve C over the complex numbers and a coordinate data around the identity, we achieve this computation by proving that the $T$-equivariant elliptic cohomology theory $EC_T$ built in [Gre05], and the $T^2$-equivariant elliptic cohomology theory $EC_{T^2}$ built in [Bar22] are 1x$T$-split. This result allows us to reduce the computation of $EC_T(CP(V))$ to the computation of $T^2$-elliptic cohomology of spheres of complex representations, already performed in [Bar22].
