The cohomology of free loop spaces of rank 2 flag manifolds

2018/03/11 by Matthew Burfitt, Burfitt, Matthew I., Jelena Grbić +1
Mathematics · Medicine · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders

paper · pdf · doi:10.48550/arxiv.1803.03923

openalex publication_date 2018/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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)/T², Sp(2)/T², Spin(4)/T², Spin(5)/T² and G₂/T². In this paper we calculate the cohomology of the free loop space of rank 2 complete flag manifolds.

Related

• The cohomology of free loop spaces of homogeneous spaces
• The cohomology of the free loop spaces of SU(n+1)/Tⁿ
• Cohomology of complete unordered flag manifolds
• The integral Pontrjagin homology of the based loop space on a flag manifold
• The graph cohomology ring of the GKM graph of a flag manifold of type G₂