Yoav Moriah
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Yoav Moriah has a total of 28 co-authors. Here are the top co-authors by number of shared publications:
- Martin Lustig
Centre de Mathématiques et Informatique, Aix-Marseille Université, 39, rue F. Joliot Curie, 13453 Marseille 13, France
6 shared publications - Eric Sedgwick
DePaul University
3 shared publications - Saul Schleimer
University of Warwick, Coventry, UK
3 shared publications - Yair N. Minsky
Yale University, New Haven, USA
3 shared publications - Jesse Johnson
Oklahoma State University
2 shared publications - Martin Lustig
Mathématiques (LATP), Université d'Aix-Marseille III, Av. Escad. Normandie-Niemen, 13397 Marseille 20, France
2 shared publications
Latest Publications
- Open Access
- 22 September 2025
- Published by Mathematical Sciences Publishers in Geometry & Topology
- Vol. 29 (6) , 3271-3343
Tunnel number one knots satisfy the Berge conjecture
Tunnel number one knots satisfy the Berge conjecture
- 22 September 2025
- Published by Mathematical Sciences Publishers in Geometry & Topology
- Vol. 29 (6) , 3271-3343
Open AccessTunnel number one knots satisfy the Berge conjecture
Tunnel number one knots satisfy the Berge conjecture
- Open Access
Tunnel number one knots satisfy the Berge Conjecture
Let $K$ be a tunnel number one knot in $M$, where $M$ is either $S^3$, or a connected sum of $S^2\times S^1$ with any lens space. (In particular this includes $M = S^2\times S^1$.) We prove that if a Dehn surgery on $K$ yields a non-trivial lens space, then $K$ is a doubly primitive knot in $M$. For $M = S^3$ this resolves the tunnel number one Berge Conjecture. For $M = S^2\times S^1$ this resolves a conjecture of Greene and Baker-Buck-Lecuona for tunnel number one knots.Open AccessTunnel number one knots satisfy the Berge Conjecture
Let $K$ be a tunnel number one knot in $M$, where $M$ is either $S^3$, or a connected sum of $S^2\times S^1$ with any lens space. (In particular this includes $M = S^2\times S^1$.) We prove that if a Dehn surgery on $K$ yields a non-trivial lens space, then $K$ is a doubly primitive knot in $M$. For $M = S^3$ this resolves the tunnel number one Berge Conjecture. For $M = S^2\times S^1$ this resolves a conjecture of Greene and Baker-Buck-Lecuona for tunnel number one knots. - Open Access
Diagram uniqueness for highly twisted knots
In this paper we prove that if a knot or link has a sufficiently complicated plat projection, then that plat projection is unique. More precisely, if a knot or link has a $2m$-plat projection, where $m$ is at least 3, each twist region of the plat contains at least three crossings, and $n$, the length of the plat, satisfies $n>4m(m-2)$, then such a projection is unique up to obvious rotations. In particular, this projection gives a canonical form for such knots and links, and thus provides a classification of these links.Open AccessDiagram uniqueness for highly twisted knots
In this paper we prove that if a knot or link has a sufficiently complicated plat projection, then that plat projection is unique. More precisely, if a knot or link has a $2m$-plat projection, where $m$ is at least 3, each twist region of the plat contains at least three crossings, and $n$, the length of the plat, satisfies $n>4m(m-2)$, then such a projection is unique up to obvious rotations. In particular, this projection gives a canonical form for such knots and links, and thus provides a classification of these links. - Open Access
Bridge distance and plat projections
We calculate the bridge distance for $m$-bridge knots/links in the $3$-sphere with sufficiently complicated $2m$-plat projections. In particular we show that if the underlying braid of the plat has $n - 1$ rows of twists and all its exponents have absolute value greater than or equal to three then the distance of the bridge sphere is exactly $\lceil n/(2(m - 2)) \rceil$, where $\lceil x \rceil$ is the smallest integer greater than or equal to $x$. As a corollary, we conclude that if such a diagram has more than $4m(m-2)$ rows then the bridge sphere defining the plat projection is the unique minimal bridge sphere for the knot.Open AccessBridge distance and plat projections
We calculate the bridge distance for $m$-bridge knots/links in the $3$-sphere with sufficiently complicated $2m$-plat projections. In particular we show that if the underlying braid of the plat has $n - 1$ rows of twists and all its exponents have absolute value greater than or equal to three then the distance of the bridge sphere is exactly $\lceil n/(2(m - 2)) \rceil$, where $\lceil x \rceil$ is the smallest integer greater than or equal to $x$. As a corollary, we conclude that if such a diagram has more than $4m(m-2)$ rows then the bridge sphere defining the plat projection is the unique minimal bridge sphere for the knot. - 1 January 2012
- Published by Walter de Gruyter GmbH in Journal für die reine und angewandte Mathematik (Crelles Journal)
- Vol. 2012 (670)
Are large distance Heegaard splittings generic?
27 pages 5 figuresInternational audienceIn a previous paper we introduced a notion of "genericity" for countable sets of curves in the curve complex of a surface S, based on the Lebesgue measure on the space of projective measured laminations in S. With this definition we prove that for each fixed g > 1 the set of irreducible genus g Heegaard splittings of high distance is generic, in the set of all irreducible Heegaard splittings. Our definition of "genericity" is different and more intrinsic then the one given via random walks
- 1 January 2012
- Published by Walter de Gruyter GmbH in Journal für die reine und angewandte Mathematik (Crelles Journal)
- Vol. 2012 (670)
Are large distance Heegaard splittings generic?
27 pages 5 figuresInternational audienceIn a previous paper we introduced a notion of "genericity" for countable sets of curves in the curve complex of a surface S, based on the Lebesgue measure on the space of projective measured laminations in S. With this definition we prove that for each fixed g > 1 the set of irreducible genus g Heegaard splittings of high distance is generic, in the set of all irreducible Heegaard splittings. Our definition of "genericity" is different and more intrinsic then the one given via random walks
- 23 November 2010
- Published by Mathematical Sciences Publishers in Algebraic & Geometric Topology
- Vol. 10 (4) , 2251-2275
Heegaard splittings with large subsurface distances
We show that sub-surfaces of a Heegaard surface for which the relative Hempel distance of the splitting is sufficiently high have to appear in any Heegaard surface of genus bounded by half that distance.Comment: 23 pages and 5 figure
- 23 November 2010
- Published by Mathematical Sciences Publishers in Algebraic & Geometric Topology
- Vol. 10 (4) , 2251-2275
Heegaard splittings with large subsurface distances
We show that sub-surfaces of a Heegaard surface for which the relative Hempel distance of the splitting is sufficiently high have to appear in any Heegaard surface of genus bounded by half that distance.Comment: 23 pages and 5 figure
- Open Access
Are large distance Heegaard splittings generic ?
In a previous paper we introduced a notion of "genericity" for countable sets of curves in the curve complex of a surface S, based on the Lebesgue measure on the space of projective measured laminations in S. With this definition we prove that for each fixed g > 1 the set of irreducible genus g Heegaard splittings of high distance is generic, in the set of all irreducible Heegaard splittings. Our definition of "genericity" is different and more intrinsic then the one given via random walks.
Open AccessAre large distance Heegaard splittings generic ?
In a previous paper we introduced a notion of "genericity" for countable sets of curves in the curve complex of a surface S, based on the Lebesgue measure on the space of projective measured laminations in S. With this definition we prove that for each fixed g > 1 the set of irreducible genus g Heegaard splittings of high distance is generic, in the set of all irreducible Heegaard splittings. Our definition of "genericity" is different and more intrinsic then the one given via random walks.
- Open Access
Horizontal Dehn Surgery and genericity in the curve complex
We introduce a general notion of "genericity" for countable subsets of a space with Borel measure, and apply it to the set of vertices in the curve complex of a surface S, interpreted as subset of the space of projective measured laminations in S, equipped with its natural Lebesgue measure. We prove that, for any 3-manifold M, the set of curves c on a Heegaard surface S in M, such that every non-trivial Dehn twist at c yields a Heegaard splitting of high distance, is generic in the set of all essential simple closed curves on S. Our definition of "genericity" is different and more intrinsic than alternative such existing notions, given e.g. via random walks or via limits of quotients of finite sets.
Open AccessHorizontal Dehn Surgery and genericity in the curve complex
We introduce a general notion of "genericity" for countable subsets of a space with Borel measure, and apply it to the set of vertices in the curve complex of a surface S, interpreted as subset of the space of projective measured laminations in S, equipped with its natural Lebesgue measure. We prove that, for any 3-manifold M, the set of curves c on a Heegaard surface S in M, such that every non-trivial Dehn twist at c yields a Heegaard splitting of high distance, is generic in the set of all essential simple closed curves on S. Our definition of "genericity" is different and more intrinsic than alternative such existing notions, given e.g. via random walks or via limits of quotients of finite sets.
- 1 March 2009
- Published by Elsevier in Topology and its Applications
- Vol. 156 (6) , 1118-1129
High distance Heegaard splittings via fat train tracks
- 1 March 2009
- Published by Elsevier in Topology and its Applications
- Vol. 156 (6) , 1118-1129
High distance Heegaard splittings via fat train tracks
- Open Access
High distance Heegaard splittings via fat train tracks
We define "fat" train tracks and use them to give a combinatorial criterion for the Hempel distance of Heegaard splittings for closed orientable 3-manifolds. We apply this criterion to 3-manifolds obtained from surgery on knots in the three sphere.
Open AccessHigh distance Heegaard splittings via fat train tracks
We define "fat" train tracks and use them to give a combinatorial criterion for the Hempel distance of Heegaard splittings for closed orientable 3-manifolds. We apply this criterion to 3-manifolds obtained from surgery on knots in the three sphere.