Zobrazeno 1 - 10
of 81
pro vyhledávání: '"Kofman, Ilya"'
Autor:
Champanerkar, Abhijit, Kofman, Ilya
Dasbach and Lin proved a "volumish theorem" for alternating links. We prove the analogue for alternating link diagrams on surfaces, which provides bounds on the hyperbolic volume of a link in a thickened surface in terms of coefficients of its reduce
Externí odkaz:
http://arxiv.org/abs/2010.08499
Publikováno v:
Algebr. Geom. Topol. 22 (2022) 739-784
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 polyhedra is
Externí odkaz:
http://arxiv.org/abs/1910.13131
Autor:
Kim, Seungwon, Kofman, Ilya
Publikováno v:
Encyclopedia of Knot Theory, Chapman and Hall/CRC (2021), Chapter 25
An expository article on Turaev surfaces written for "A Concise Encyclopedia of Knot Theory," to appear.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/1901.09995
Autor:
Champanerkar, Abhijit, Kofman, Ilya
Publikováno v:
Acta Math Vietnam (2021)
We provide examples of towers of covers of cusped hyperbolic 3-manifolds whose exponential homological torsion growth is explicitly computed in terms of volume growth. These examples arise from abelian covers of alternating links in the thickened tor
Externí odkaz:
http://arxiv.org/abs/1901.07494
Publikováno v:
J. London Math. Soc. (2) 99 (2019), 872-900
The Vol-Det Conjecture relates the volume and the determinant of a hyperbolic alternating link in $S^3$. We use exact computations of Mahler measures of two-variable polynomials to prove the Vol-Det Conjecture for many infinite families of alternatin
Externí odkaz:
http://arxiv.org/abs/1805.05490
Publikováno v:
J. London Math. Soc. (2) 99 (2019), 807-830
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 correspondin
Externí odkaz:
http://arxiv.org/abs/1802.05343
Autor:
Champanerkar, Abhijit, Kofman, Ilya
Publikováno v:
New York J. Math. 22 (2016) 891-906
Let L be any infinite biperiodic alternating link. We show that for any sequence of finite links that Folner converges almost everywhere to L, their determinant densities converge to the Mahler measure of the 2-variable characteristic polynomial of t
Externí odkaz:
http://arxiv.org/abs/1604.03795
Publikováno v:
J. Knot Theory Ramifications, 25 (2016), no. 3, 1640001[1-11]
We recently discovered a relationship between the volume density spectrum and the determinant density spectrum for infinite sequences of hyperbolic knots. Here, we extend this study to new quantum density spectra associated to quantum invariants, suc
Externí odkaz:
http://arxiv.org/abs/1506.05841
Publikováno v:
Algebr. Geom. Topol. 16 (2016) 3301-3323
Weaving knots are alternating knots with the same projection as torus knots, and were conjectured by X.-S. Lin to be among the maximum volume knots for fixed crossing number. We provide the first asymptotically correct volume bounds for weaving knots
Externí odkaz:
http://arxiv.org/abs/1506.04139
Publikováno v:
J. London Math. Soc. 94 (2016), no. 3, 883-908
The ratio of volume to crossing number of a hyperbolic knot is known to be bounded above by the volume of a regular ideal octahedron, and a similar bound is conjectured for the knot determinant per crossing. We investigate a natural question motivate
Externí odkaz:
http://arxiv.org/abs/1411.7915