2017/06/30 by Matthew Burfitt, Burfitt, Matthew
Mathematics · Physics and Astronomy · #Algebraic Topology (math.AT) #Black Holes and Theoretical Physics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1706.10258
openalex publication_date 2017/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The free loops space ΛX of a space X has become an important object of study particularly in the case when X is a manifold.The study of free loop spaces is motivated in particular by two main examples. The first is their relation to geometrically distinct periodic geodesics on a manifold, originally studied by Gromoll and Meyer in 1969. More recently the study of string topology and in particular the Chas-Sullivan loop product has been an active area of research. A complete flag manifold is the quotient of a Lie group by its maximal torus and is one of the nicer examples of a homogeneous space. Both the cohomology and Chas-Sullivan product structure are understood for spaces Sn, ℂPn and most simple Lie groups. Hence studying the topology of the free loops space on homogeneous space is a natural next step. In the thesis we compute the differentials in the integral Leray-Serre spectral sequence associated to the free loops space fibrations in the cases of SU(n+1)/Tn and Sp(n)/Tn. Study in detail the structure of the third page of the spectral sequence in the case of SU(n) and give the module structure of H^*(Λ(SU(3)/T2);ℤ) and H^*(Λ(Sp(2)/T2);ℤ).