Work

The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4

Year: 2025

Type: article

Abstract: Let $M$ be a closed connected spin manifold. Index theory provides a topological lower bound on the dimension of the kernel of the Dirac operator which depends on the choice of Riemannian metric. Riemannian metrics for which this bound is attained are called Dirac-minimal. We show that the space of Dirac-minimal metrics on $M$ is connected if $M$ is of dimension 2 or 4.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2025.102

Authors: Universität Regensburg, Germany, Bernd Ammann, Mattias Dahl, Kungliga Tekniska Högskolan, Sweden

Institutions: University of Regensburg, KTH Royal Institute of Technology

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Deutsche Forschungsgemeinschaft, Universität Regensburg

Awards: G2418827033, G5741529951