The cohomology of free loop spaces of rank 2 flag manifolds

TL;DR

This paper computes the cohomology of the free loop spaces of rank 2 complete flag manifolds, providing a comprehensive understanding of their topological structure.

Contribution

It offers the first complete calculation of the cohomology of free loop spaces for all rank 2 complete flag manifolds.

Findings

Cohomology groups of free loop spaces are explicitly determined.

Results apply to manifolds like SU(3)/T^2, Sp(2)/T^2, Spin(4)/T^2, Spin(5)/T^2, G_2/T^2.

Enhances understanding of the topology of flag manifolds and their loop spaces.

Abstract

A complete flag manifold is the quotient of a Lie group by its maximal torus. The rank of a flag manifold is the dimension of the maximal torus of the Lie group. The rank 2 complete flag manifolds are $SU(3)/T^2$, $Sp(2)/T^2$, $Spin(4)/T^2$, $Spin(5)/T^2$ and $G_2/T^2$. In this paper we calculate the cohomology of the free loop space of rank 2 complete flag manifolds.