Related papers: The volume of hyperbolic alternating link compleme…
To any prime alternating link, we associate a collection of hyperbolic right-angled ideal polyhedra by relating geometric, topological and combinatorial methods to decompose the link complement. The sum of the hyperbolic volumes of these…
The hyperbolic volume of a link complement is known to be unchanged when a half-twist is added to a link diagram, and a suitable 3-punctured sphere is present in the complement. We generalize this to the simplicial volume of link…
We show that for a large class of hyperbolic knots and links, we can determine bounds on the volume of the link complement from combinatorial information given by a link diagram. Specifically, there is a universal constant C such that if a…
Augmented alternating links are links obtained by adding trivial components that bound twice-punctured disks to non-split reduced non-2-braid prime alternating projections. These links are known to be hyperbolic. Here, we extend to show…
A finite-volume hyperbolic 3-manifold geometrically bounds if it is the geodesic boundary of a finite-volume hyperbolic 4-manifold. We construct here an example of non-compact, finite-volume hyperbolic 3-manifold that geometrically bounds.…
We give a refined upper bound for the hyperbolic volume of an alternating link in terms of the first three and the last three coefficients of its colored Jones polynomial.
Let $\Delta_{L,\rho_n}(t)$ be the twisted Alexander polynomial with respect to the representation given by the composition of the lift of the holonomy representation of a certain hyperbolic link $L$ and the $n$-dimensional irreducible…
The work of Jorgensen and Thurston shows that there is a finite number N(v) of orientable hyperbolic 3-manifolds with any given volume v. We show that there is an infinite sequence of closed orientable hyperbolic 3-manifolds, obtained by…
We view closed orientable 3-manifolds as covers of S^3 branched over hyperbolic links. For a p-fold cover M \to S^3, branched over a hyperbolic link L, we assign the complexity p Vol(S^3 minus L) (where Vol is the hyperbolic volume). We…
We show that the volumes of certain hyperbolic A-adequate links can be bounded (above and) below in terms of two diagrammatic quantities: the twist number and the number of certain alternating tangles in an A-adequate diagram. We then…
We consider hyperbolic links that admit alternating projections on surfaces in compact, irreducible 3-manifolds. We show that, under some mild hypotheses, the volume of the complement of such a link is bounded below in terms of a Kauffman…
We prove that the 8^4_2 link complement is the minimal volume orientable hyperbolic manifold with 4 cusps. Its volume is twice of the volume V_8 of the ideal regular octahedron, i.e. 7.32... = 2V_8. The proof relies on Agol's argument used…
The Vol-Det Conjecture, formulated by Champanerkar, Kofman and Purcell, states that there exists a specific inequality connecting the hyperbolic volume of an alternating link and its determinant. Among the classes of links for which this…
W. Thurston suggested a method for computing hyperbolic volume of hyperbolic 3-manifolds, based on a triangulation of the manifold. The method was implemented by J. Weeks in the program SnapPea, which produces a decimal approximation as a…
For $D$ a reduced alternating surface link diagram, we bound the twist number of $D$ in terms of the coefficients of a polynomial invariant. To this end, we introduce a generalization of the homological Kauffman bracket defined by Krushkal.…
A biperiodic alternating link has an alternating quotient link in the thickened torus. In this paper, we focus on semi-regular links, a class of biperiodic alternating links whose hyperbolic structure can be immediately determined from a…
The volume density of a hyperbolic link is defined as the ratio of hyperbolic volume to crossing number. We study its properties and a closely-related invariant called the determinant density. It is known that the sets of volume densities…
We prove that for any V>0, there exist a hyperbolic manifold M_V, so that Vol(M_V) < 2.03 and LinVol(M_V) > V. The proof requires study of cosmetic surgery on links (equivalently, fillings of manifolds with boundary tori). There is no bound…
We show that the cusp volume of a hyperbolic alternating knot can be bounded above and below in terms of the twist number of an alternating diagram of the knot. This leads to diagrammatic estimates on lengths of slopes, and has some…
This paper investigates a real-valued topological invariant of 3-manifolds called topological volume. For a given 3-manifold M it is defined as the smallest volume of the complement of a (possibly empty) hyperbolic link in M. Various…