Related papers: Boundary-reducing surgeries and bridge number
Let N be a compact, orientable hyperbolic 3-manifold with connected, totally geodesic boundary of genus 2. If N has Heegaard genus at least 5, then its volume is greater than 6.89. The proof of this result uses the following dichotomy:…
We study compact three-manifolds with boundary obtained by randomly gluing together truncated tetrahedra along their faces. We prove that, asymptotically almost surely as the number of tetrahedra tends to infinity, these manifolds are…
We investigate the class of $3$-decomposable genus two handlebody-knots and provide a complete classification of essential annuli in their exteriors. We introduce the notion of $\tau$- and $\rho$-tangles and good rectangles and annuli. By…
A knot is called an L-space knot if it admits a positive Dehn surgery yielding an L-space. In the SnapPy census, there are exactly 9 asymmetric L-space knots. Among them, the knot t12533 is the only known example of braid index 4. We…
It is known that any tame hyperbolic 3-manifold with infinite volume and a single end is the geometric limit of a sequence of finite volume hyperbolic knot complements. Purcell and Souto showed that if the original manifold embeds in the…
This paper introduces a rigorous computer-assisted procedure for analyzing hyperbolic 3-manifolds. This technique is used to complete the proof of several long-standing rigidity conjectures in 3-manifold theory as well as to provide a new…
The classification of finite group-actions on closed surfaces of small genus is well-known. In the present paper we are interested in the question of which of these group-actions are bounding (extend to a compact 3-manifold with the surface…
Any two geometric ideal triangulations of a cusped complete hyperbolic $3$-manifold $M$ are related by a sequence of Pachner moves through topological triangulations. We give a bound on the length of this sequence in terms of the total…
We give a complete classification of exceptional surgeries on hyperbolic alternating knots in the 3-sphere. As an appendix, we also show that the Montesinos knots M (-1/2, 2/5, 1/(2q + 1)) with q at least 5 have no non-trivial exceptional…
In this paper we derive explicit estimates for the functions which appear in the previous work of Bridgeman and Kahn. As a consequence, we obtain an explicit lower bound for the length of the shortest orthogeodesic in terms of the volume of…
We give an upper bound on the distance between a degeneracy slope for a very full essential lamination and a boundary slope of an essential surface embedded in a compact, orientable, irreducible, atoroidal 3-manifold with incompressible…
A Seifert surface F for a knot K is free if the complement of F is a handlebody (i.e., has free fundamental group). The free genus of K is the minimum genus among all free Seifert surfaces for K. In this paper we show that there exist…
We discuss an alternative approach to the uniformisation problem on surfaces with boundary by representing conformal structures on surfaces $M$ of general type by hyperbolic metrics with boundary curves of constant positive geodesic…
We give a necessary and sufficient condition for a simple closed curve on the boundary of a genus two handlebody to decompose the handlebody into (torus with one boundary component times [0,1]. We use this condition to decide whether a…
Let $C(2n, 3)$ be the family of two bridge knots of slope $(4n+1)/(6n+1)$. We calculate the volumes of the $C(2n, 3)$ cone-manifolds using the Schl\"{a}fli formula. We present the concrete and explicit formula of them. We apply the general…
We give a diagrammatic characterization of the $(1,1)$ knots in the three-sphere and lens spaces which admit large Dehn surgeries to manifolds with Heegaard Floer homology of next-to-minimal rank. This is inspired by a corresponding result…
In this paper, we prove the Bounded Height Conjecture which the author formulated in [2]. As a corollary, it follows that there are only a finite number of hyperbolic three manifolds of bounded volume and trace field degree.
In this note, we show that there exist cusped hyperbolic $3$-manifolds that embed geodesically, but cannot bound geometrically. Thus, being a geometric boundary is a non-trivial property for such manifolds. Our result complements the work…
We show that if there exists a knot in $S^3$ that admits purely cosmetic surgeries, then there exists a hyperbolic one with this property.
We summarize and expand known connections between the study of Dehn surgery on links and the study of trisections of closed, smooth 4-manifolds. In addition, we describe how the potential counterexamples to the Generalized Property R…