Semi-adequate closed braids and volume

Giambrone, Adam

doi:10.1016/j.topol.2015.10.009

Cited by 2 publications

(2 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several families of hyperbolic links in S 3 , including alternating ones, satisfy a "coarse volume conjecture": coefficients of the Jones and colored Jones polynomials provide two-sided linear bounds of the volume of the link complement [9,[13][14][15][16][17]25]. The next theorem provides a similar result for alternating links in thickened surfaces and there is a similar result for links with alternating projections on Heegaard tori in lens spaces (see Corollary 4.2).…”

mentioning

confidence: 84%

Guts, volume and skein modules of 3-manifolds

Bavier

Kalfagianni

2022

Fund. Math.

View full text Add to dashboard Cite

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 bracket function defined on link diagrams on the surface.In the case that the 3-manifold is a thickened surface, this Kauffman bracket function leads to a Jones-type polynomial that is an isotopy invariant of links. We show that coefficients of this polynomial provide 2-sided linear bounds on the volume of hyperbolic alternating links in the thickened surface. As a corollary of the proof of this result, we deduce that the twist number of a reduced, twist-reduced, alternating link projection with checkerboard disk regions is an invariant of the link.

show abstract

mentioning

confidence: 84%

Guts, volume and skein modules of 3-manifolds

Bavier

Kalfagianni

2022

Fund. Math.

View full text Add to dashboard Cite

show abstract

“…Several families of hyperbolic links in S 3 , including alternating ones, are known to satisfy a "coarse volume conjecture": coefficients of the Jones and colored Jones polynomial provide two-sided linear bounds of the volume of the link complement [9,[12][13][14][15][16]23]. The next theorem provides a similar result for alternating links in thickened surfaces and there is a similar result for links with alternating projections on Heegaard tori in Lens spaces (see 4.2 ).…”

Section: Introductionmentioning

confidence: 99%

Guts, volume and Skein Modules of 3-manifolds

Bavier¹,

Kalfagianni²

2020

Preprint

View full text Add to dashboard Cite

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 bracket function defined on link diagrams on the surface.In the case that the 3-manifold is a thickened surface, this Kauffman bracket function leads to a Jones-type polynomial that is an isotopy invariant of links. We show that coefficients of this polynomial provide 2-sided linear bounds on the volume of hyperbolic alternating links in the thickened surface. As a corollary of the proof of this result, we deduce that the twist number of a reduced, twist reduced, alternating link projection with checkerboard disk regions, is an invariant of the link.

show abstract

Semi-adequate closed braids and volume

Cited by 2 publications

References 16 publications

Guts, volume and skein modules of 3-manifolds

Guts, volume and skein modules of 3-manifolds

Guts, volume and Skein Modules of 3-manifolds

Contact Info

Product

Resources

About