From CT Scans to 4-Manifold Topology via Neutral Geometry

Authors

Brendan Guilfoyle, School of STEM, Munster Technological University, Kerry, Tralee, Co. Kerry, IrelandFollow

ORCID

https://orcid.org/0000-0002-7437-5046

Document Type

Article

Disciplines

Geometry and Topology | Mathematics | Physical Sciences and Mathematics

Publication Details

Irish Mathematical Society Bulletin, Summer Issue 2023 9-32. © Irish Mathematical Society.

Abstract

In this survey paper the ultrahyperbolic equation in dimension four is discussed from a geometric, analytic and topological point of view. The geometry centres on the canonical neutral metric on the space of oriented geodesics of 3-dimensional space-forms, the analysis discusses a mean value theorem for solutions of the equation and presents a new solution of the Cauchy problem over a certain family of null hypersurfaces, while the topology relates to generalizations of codimension two foliations of 4-manifolds.

Recommended Citation

Brendan Guilfoyle, From CT scans to 4-manifold topology via neutral geometry, Irish Math. Soc. Bulletin, Number 91, Summer 2023, 9–32, 10.33232/BIMS.0091.9.32.