2021/06/07 by Matthew Burfitt, Burfitt, Matthew I., Jelena Grbić +1
Computer Science · Mathematics · Physics and Astronomy · #05E05 (Secondary) #13P10 #55P35 (Primary) 14M15 #55T10 #Advanced Differential Equations and Dynamical Systems #Algebraic Topology (math.AT) #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2106.03440
openalex publication_date 2021/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the cohomology of the free loop space of SU(n+1)/Tn, the simplest example of a complete flag manifolds and an important homogeneous space. Through this enhanced analysis we reveal rich new combinatorial structures arising in the cohomology algebra of the free loop spaces. We build new theory to allow for the computation of H^*(Λ(SU(n+1)/Tn);ℤ), a significantly more complicated structure than other known examples. In addition to our theoretical results, we explicitly implement a novel integral Gröbner basis procedure for computation. This procedure is applicable to any Leray-Serre spectral sequence for which the cohomology of the base space is the quotient of a finitely generated polynomial algebra. The power of this procedure is illustrated by the explicit calculation of H^*( Λ(SU(4)/T3);ℤ). We also provide a python library with examples of all procedures used in the paper.