Systolic geometry and regularization technique

2015/06/25 by Guillaume Bulteau, Bulteau, Guillaume
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1506.07848

openalex publication_date 2015/06/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The aim of this text is to present the concept of systole of a compact riemannian manifold and to give an overview of systolic geometry. I will also present the "regularization technique", which leads to major results in systolic geometry. I will detail how this technique allows to link the systolic volume of some closed riemannian manifolds to homotopical invariants of these manifolds, such as the Betti numbers (according to Gromov) and the minimal entropy (according to Sabourau).

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