Lectures on families of Dirac operators and applications

2022/09/03 by Francesco Lin, Lin, Francesco
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2209.01467

openalex publication_date 2022/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

These are the notes for a minicourse taught at the 2022 ICTP summer school `Frontiers in Geometry and Topology'. The goal is to introduce families of Dirac operators and how they can be used to study interactions between geometry and topology. In particular, we discuss the index theorem for families of twisted Dirac operators, and its applications to metrics of positive scalar curvature and the three-dimensional Weinstein conjecture.

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