Rational circle-equivariant elliptic cohomology of CP(V)

Matteo Barucco

Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 49-78.

Résumé

$\def\T{\mathbb{T}}\def\CPV{\mathbb{C}P(V)}$

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.

Détail

DOI : 10.4310/HHA.2024.v26.n2.a3

Classification : 55N34, 55N91
Keywords: equivariant elliptic cohomology, algebraic model, complex projective space