Add to ORKGFor every integer $g\ge 2$ we construct 3-dimensional genus-$g$ 1-handlebodies smoothly embedded in $S^4$ with the same boundary, and which are defined by the same cut systems of their boundary, yet which are not isotopic rel. boundary via any locally flat isotopy even when their interiors are pushed into $B^5$. This proves a conjecture of Budney and Gabai for genus at least 2.Comment: 8 pages, 1 figure. Incorporated referee comments, streamlined paper, added citation to Hartman and discussion of boundary-parallel codimension-2 balls in high dimensions to the introductio
We show that, for hyperbolic fibred knots in the three-sphere, the volume and the genus are unrelate...
For $n\ge 4$, we show that there are infinitely many formally contact isotopic embeddings of $(ST^*S...
AbstractWe discuss the diagrammatic theory of knot isotopies in dimension 4. We project a knotted su...
We describe an algorithm to decide whether two genus-two surfaces embedded in the 3-sphere are isoto...
If H is a spatial handlebody, i.e. a handlebody embedded in the 3-sphere, a spine of H is a graph Γ...
We provide three 3-dimensional characterizations of the Z-slice genus of a knot, the minimal genus o...
We study smooth, proper embeddings of noncompact surfaces in 4-manifolds, focusing on exotic planes ...
We study locally flat, compact, oriented surfaces in 4-manifolds whose exteriors have infinite cycl...
A knotted surface in the 4-sphere may be described by means of a hyperbolic diagram that captures th...
In this note, we show that if two surfaces in are homeomorphic, then a simple and purely topological...
We combine Freedman's topology with Eliashberg's holomorphic theory to construct Stein neighborhood ...
AbstractAn infinite family of inequivalent genus 2 handlebodies embedded in S3 is described, all of ...
This thesis is a comparison of the smooth and topological categories in dimension 4. We first discus...
In an earlier work, we introduced a family of t-modified knot Floer homologies, defined by modifying...
David Gabai recently proved a smooth 4-dimensional "Light Bulb Theorem" in the absence of 2-torsion ...
We show that, for hyperbolic fibred knots in the three-sphere, the volume and the genus are unrelate...
For $n\ge 4$, we show that there are infinitely many formally contact isotopic embeddings of $(ST^*S...
AbstractWe discuss the diagrammatic theory of knot isotopies in dimension 4. We project a knotted su...
We describe an algorithm to decide whether two genus-two surfaces embedded in the 3-sphere are isoto...
If H is a spatial handlebody, i.e. a handlebody embedded in the 3-sphere, a spine of H is a graph Γ...
We provide three 3-dimensional characterizations of the Z-slice genus of a knot, the minimal genus o...
We study smooth, proper embeddings of noncompact surfaces in 4-manifolds, focusing on exotic planes ...
We study locally flat, compact, oriented surfaces in 4-manifolds whose exteriors have infinite cycl...
A knotted surface in the 4-sphere may be described by means of a hyperbolic diagram that captures th...
In this note, we show that if two surfaces in are homeomorphic, then a simple and purely topological...
We combine Freedman's topology with Eliashberg's holomorphic theory to construct Stein neighborhood ...
AbstractAn infinite family of inequivalent genus 2 handlebodies embedded in S3 is described, all of ...
This thesis is a comparison of the smooth and topological categories in dimension 4. We first discus...
In an earlier work, we introduced a family of t-modified knot Floer homologies, defined by modifying...
David Gabai recently proved a smooth 4-dimensional "Light Bulb Theorem" in the absence of 2-torsion ...
We show that, for hyperbolic fibred knots in the three-sphere, the volume and the genus are unrelate...
For $n\ge 4$, we show that there are infinitely many formally contact isotopic embeddings of $(ST^*S...
AbstractWe discuss the diagrammatic theory of knot isotopies in dimension 4. We project a knotted su...