6 papers
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…
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…
Grasper families of spheres in and barbell diffeomorphisms of
Eduardo Fernández, David T. Gay, Daniel Hartman +1
We show that the fundamental group of framed circles in injects into the fundamental group of framed spheres in , so that the cokernel is the fundam…
On Watanabe's theta graph diffeomorphism in the 4-sphere
David T. Gay
Watanabe's theta graph diffeomorphism, constructed using Watanabe's clasper surgery construction which turns trivalent graphs in 4-manifolds into parameterized families of diffeomo…
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…
On Dividing a Rectangle
Robert Dumitru, Quinn Perian, Alexander Nealey +7
This paper deals with the history of the following problem: "Can an arbitrary rectangle be dissected into 3 non-rectangular congruent regions?" We present a new elementary proof th…