David Gay

collaborators

4 papers

math.GT2026

Pseudo-Isotopy and Diffeomorphisms of the 4-Sphere I: Loops of Spheres

David Gabai, David T. Gay, Daniel Hartman

We introduce new methods in pseudo-isotopy and embedding space theory. As an application we introduce an invariant that detects nontrivial loops of embedded 2-spheres in $S^{2} \ti…

math.GT2026

Morse diagrams, Murasugi sums, and the mapping class group

Jack Brand, David Gay, Joan Licata

A combinatorial Morse structure encodes a mapping class for a surface with boundary, and the data may be efficiently represented via a Morse diagram. This diagram determines an ope…

math.GT2026

Pseudo-isotopies of simply connected 4-manifolds

David Gabai, David T. Gay, Daniel Hartman +2

Perron and Quinn gave independent proofs in 1986 that every topological pseudo-isotopy of a simply-connected, compact topological 4-manifold is isotopic to the identity. Another re…

math.GT2024

Grasper families of spheres in $S^{2} \times D^{2}$ and barbell diffeomorphisms of $S^{1} \times S^{2} \times I$

Eduardo FernÃ¡ndez, David T. Gay, Daniel Hartman +1

We show that the fundamental group of framed circles in $S^{1} \times D^{3}$ injects into the fundamental group of framed spheres in $S^{2} \times D^{2}$ , so that the cokernel is the fundam…

Pseudo-Isotopy and Diffeomorphisms of the 4-Sphere I: Loops of Spheres

Morse diagrams, Murasugi sums, and the mapping class group

Pseudo-isotopies of simply connected 4-manifolds

Grasper families of spheres in S2×D2 and barbell diffeomorphisms of S1×S2×I

Grasper families of spheres in $S^{2} \times D^{2}$ and barbell diffeomorphisms of $S^{1} \times S^{2} \times I$