Scalar Curvature Constraints on Symplectic 4-Manifolds
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Authors
Galloway, Brian
Issue Date
2025
Type
Thesis
Language
en_US
Keywords
Dirac operatior , scalar curvature , spin geometry , symplectic manifolds
Alternative Title
Abstract
This thesis presents a remarkable result, that showcases an unexpected interplaybetween Riemannian geometry and symplectic topology on 4-manifolds. These two
branches of mathematics belong to different worlds: Where geometry concerns it-
self with distances, angles, areas, curvatures, etc., all of which typically vary from
one point on the manifold to the next, topology studies properties of manifolds that
are unaltered and remain constant when varying the metric. In this thesis we first
provide a general overview of spin geometry on Riemannian manifolds and then es-
tablish a fundamental restriction on the scalar curvature induced by the topology of
a symplectic manifold.