Scalar Curvature Constraints on Symplectic 4-Manifolds

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.

Level thesis:degree_level

Master's Degree

Year dc:date.issued

2025

Author dc:creator

• Galloway, Brian

Advisor dc:contributor.advisor

• Jabuka, Stanislav

Committee members dc:contributor.committeemember

• Herald, Christopher
• Tavakkoli, Alireza

• Dirac operatior
• scalar curvature
• spin geometry
• symplectic manifolds

Language dc:language.iso

en_US, English

Repository record dc:identifier.uri

https://scholarwolf.unr.edu/handle/11714/11605

OAI identifier oai:identifier

oai:scholarwolf.unr.edu:11714/11605