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.

Keywords

equivariant elliptic cohomology, algebraic model, complex projective space

2010 Mathematics Subject Classification

55N34, 55N91

Full Text (PDF format)

Received 15 November 2022

Received revised 27 July 2023

Accepted 27 July 2023

Published 18 September 2024