scholarly journals Complex length of short curves and Minimal Fibrations of hyperbolic three‐Manifolds fibering over the circle

2018 ◽  
Vol 118 (6) ◽  
pp. 1305-1327 ◽  
Author(s):  
Zheng Huang ◽  
Biao Wang
Keyword(s):  
Hyperbolic Three Manifolds ◽  
Complex Length

scholarly journals Constructing 1-cusped isospectral non-isometric hyperbolic 3-manifolds

2017 ◽  
Vol 10 (01) ◽  
pp. 1-25
Author(s):  
Stavros Garoufalidis ◽  
Alan W. Reid
Keyword(s):  
Discrete Spectrum ◽  
Eisenstein Series ◽  
Finite Volume ◽  
Finite Covers ◽  
Figure Eight Knot ◽  
Complex Length

We construct infinitely many examples of pairs of isospectral but non-isometric [Formula: see text]-cusped hyperbolic [Formula: see text]-manifolds. These examples have infinite discrete spectrum and the same Eisenstein series. Our constructions are based on an application of Sunada’s method in the cusped setting, and so in addition our pairs are finite covers of the same degree of a 1-cusped hyperbolic 3-orbifold (indeed manifold) and also have the same complex length spectra. Finally we prove that any finite volume hyperbolic 3-manifold isospectral to the figure-eight knot complement is homeomorphic to the figure-eight knot complement.

scholarly journals Modelling sex-specific crossover patterning in Arabidopsis

2018 ◽  
Author(s):  
Andrew Lloyd ◽  
Eric Jenczewski
Keyword(s):  
Mechanical Model ◽  
Double Strand Breaks ◽  
Dna Double Strand Breaks ◽  
Female Meiosis ◽  
Recombination Rates ◽  
Data Set ◽  
Strand Breaks ◽  
Film Model ◽  
Chromosome Axis ◽  
Complex Length

ABSTRACTInterference is a major force governing the patterning of meiotic crossovers. A leading model describing how interference influences crossover-patterning is the beam film model, a mechanical model based on the accumulation and redistribution of crossover-promoting stress along the chromosome axis. We use the beam-film model in conjunction with a large Arabidopsis reciprocal back-cross data set to gain mechanistic insights into the differences between male and female meiosis and crossover patterning. Beam-film modelling suggests that the underlying mechanics of crossover patterning and interference are identical in the two sexes, with the large difference in recombination rates and distributions able to be entirely explained by the shorter chromosome axes in females. The modelling supports previous indications that fewer crossovers occur via the class II pathway in female meiosis and that this could be explained by reduced DNA double strand breaks in female meiosis, paralleling the observed reduction in synaptonemal complex length between the two sexes. We also demonstrate that changes in the strength of suppression of neighboring class I crossovers can have opposite effects on effective interference depending on the distance between two genetic intervals.

scholarly journals Volumes of Hyperbolic Three-Manifolds Associated with Modular Links

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1206 ◽  
Author(s):  
Alex Brandts ◽  
Tali Pinsky ◽  
Lior Silberman
Keyword(s):  
Class Group ◽  
Quadratic Field ◽  
Finite Collection ◽  
Ideal Class Group ◽  
Modular Surface ◽  
Closed Curves ◽  
Hyperbolic Three Manifolds ◽  
Unit Tangent Bundle ◽  
Real Quadratic ◽  
The Ideal

Periodic geodesics on the modular surface correspond to periodic orbits of the geodesic flow in its unit tangent bundle PSL 2 ( Z ) ∖ PSL 2 ( R ) . A finite collection of such orbits is a collection of disjoint closed curves in a 3-manifold, in other words a link. The complement of those links is always a hyperbolic 3-manifold, and hence has a well-defined volume. We present strong numerical evidence that, in the case of the set of geodesics corresponding to the ideal class group of a real quadratic field, the volume has linear asymptotics in terms of the total length of the geodesics. This is not the case for general sets of geodesics.

scholarly journals Local Mixing and Invariant Measures for Horospherical Subgroups on Abelian Covers

2018 ◽  
Vol 2019 (19) ◽  
pp. 6036-6088
Author(s):  
Hee Oh ◽  
Wenyu Pan
Keyword(s):  
Lie Group ◽  
Invariant Measures ◽  
Dense Subgroup ◽  
Abelian Cover ◽  
Rank One ◽  
Hyperbolic Three Manifolds ◽  
Abelian Covers ◽  
Prime Geodesic Theorem ◽  
Convex Cocompact ◽  
Frame Flow

Abstract Abelian covers of hyperbolic three-manifolds are ubiquitous. We prove the local mixing theorem of the frame flow for abelian covers of closed hyperbolic three-manifolds. We obtain a classification theorem for measures invariant under the horospherical subgroup. We also describe applications to the prime geodesic theorem as well as to other counting and equidistribution problems. Our results are proved for any abelian cover of a homogeneous space Γ0∖G where G is a rank one simple Lie group and Γ0 < G is a convex cocompact Zariski dense subgroup.

scholarly journals Modelling Sex-Specific Crossover Patterning in Arabidopsis

Genetics ◽  
2019 ◽  
Vol 211 (3) ◽  
pp. 847-859 ◽  
Author(s):  
Andrew Lloyd ◽  
Eric Jenczewski
Keyword(s):  
Mechanical Model ◽  
Double Strand Breaks ◽  
Dna Double Strand Breaks ◽  
Female Meiosis ◽  
Recombination Rates ◽  
Data Set ◽  
Strand Breaks ◽  
Film Model ◽  
Chromosome Axis ◽  
Complex Length

“Interference” is a major force governing the patterning of meiotic crossovers. A leading model describing how interference influences crossover patterning is the beam-film model, a mechanical model based on the accumulation and redistribution of crossover-promoting “stress” along the chromosome axis. We use the beam-film model in conjunction with a large Arabidopsis reciprocal backcross data set to gain “mechanistic” insights into the differences between male and female meiosis, and crossover patterning. Beam-film modeling suggests that the underlying mechanics of crossover patterning and interference are identical in the two sexes, with the large difference in recombination rates and distributions able to be entirely explained by the shorter chromosome axes in females. The modeling supports previous indications that fewer crossovers occur via the class II pathway in female meiosis and that this could be explained by reduced DNA double-strand breaks in female meiosis, paralleling the observed reduction in synaptonemal complex length between the two sexes. We also demonstrate that changes in the strength of suppression of neighboring class I crossovers can have opposite effects on “effective” interference depending on the distance between two genetic intervals.

The relationship between synaptonemal complex length and genome size in four vertebrate classes (Osteicthyes, Reptilia, Aves, Mammalia)

1994 ◽  
Vol 2 (2) ◽  
pp. 153-162 ◽  
Author(s):  
Daniel G. Peterson ◽  
Stephen M. Stack ◽  
Joseph L. Healy ◽  
Bryon S. Donohoe ◽  
Lorinda K. Anderson
Keyword(s):  
Synaptonemal Complex ◽  
Genome Size ◽  
The Relationship ◽  
Complex Length
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