# Degenerations Of Ideal Hyperbolic Triangulations

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### Ideal triangulations of hyperbolic 3-manifolds - bdim

Topological and hyperbolic ideal triangulations. In order to endow a degeneration of topology for partially flat solutions of C*F only. 4. Degeneration of

### Pre-publication Accepted Manuscript - American Mathematical

by M Sakuma 2018 Cited by 7 we prove that certain ideal triangulations of their complements, derived from reduced alternating diagrams, are non-degenerate, in the sense that none of for those triangulations for hyperbolic alternating links have solutions

### Hyperbolic geometry - The University of Chicago

by D CALEGARI 2019 In a similar way, the geometry of hyperbolic space is best understood by This is the only place in the argument where an ideal triangulation is the argument works just as well if some simplices are degenerate (i.e. have.

### Similarity structures on the torus and the Klein bottle via

by S Francaviglia 2006 Cited by 3 Given an ideal triangulation of M one can try to define a finite-volume hyper- It is well-known that if the moduli are all in pю and define a hyperbolic In general, a cancellation might produce a degeneration of the topology of the torus.

### An application of non-positively curved cubings of - CSI Math

by M Sakuma 2016 Cited by 7 triangulations for hyperbolic alternating links have solutions corresponding to the complete following degeneration of ideal tetrahedra occur.

### Research Statement - University of San Diego Home Pages

My research interests focus mainly on 3-manifolds, hyperbolic geometry, and ideal triangulation of the 3-manifold; the ideal tetrahedra degenerate to ideal

### Veering structures of the canonical decompositions of hyperbolic

Branched Coverings, Degenerations, and Related Topics 2016 layered ideal triangulation of the bundle. Are the veering ideal triangulations geometric?

### Essential Spunnormal Surfaces via Tropical - UIC Indigo

by A Brasile 2013 IDEAL TRIANGULATIONS AND CELL DECOMPOSITIONS. 5. 2.1 231, 2011. 22. Tillmann, S.: Degenerations of ideal hyperbolic triangulations.

### Partially flat ideal triangulations of cusped hyperbolic 3

by C Petronio 2000 Cited by 30 hyperbolic structure then it admits a degenerate geodesic ideal triangulation, in which some (but not all) of the tetrahedra are flattened out to quadrilaterals.

### Volume of representations and birationality of peripheral

by A Guilloux 2017 Cited by 6 Let M be an orientable hyperbolic manifold with one cusp (e.g. a Stephan Tillmann, Degenerations of ideal hyperbolic triangulations, Math. Z.

### A COMBINATORIAL CURVATURE FLOW FOR COMPACT 3

by F Luo 2005 Cited by 31 the complete hyperbolic metric with totally geodesic boundary on a mani Given an ideal triangulation of a compact 3-manifold with boundary consisting (1.1) which corresponds to the degeneration of the strictly hyperideal

### Ideal triangulations of 3 manifolds II - Research Institute for

by E Kang 2005 Cited by 17 existence of ideal triangulations admitting (complete) hyperbolic metrics. ples of taut ideal triangulations which do not admit an angle structure. [23] S Tillmann, Degenerations and normal surface theory, PhD thesis,

### Appendix A A Capsule of Moduli Space Theory

by M Carfora 2012 Cited by 17 ffiffiffiffiffiffiffi. ہ1 p dy;. ًA:2ق. M. Carfora and A. Marzuoli, Quantum Triangulations, Lecture Notes in Physics 845, degenerate (in particular it is not Kنhler) on [email protected] g; N0 characterization of the Poisson structure gab in terms of ideal hyperbolic.

### ON THURSTON'S SHIFT COORDINATES AND STRETCH

by A PAPADOPOULOS 2006 30F45. Keywords: Ideal triangulation, hyperbolic structure, horocyclic folia- is useful for studying degenerations of hyperbolic surfaces.

### The Toric Geometry of Triangulated Polygons in - UMD MATH

by B Howard Cited by 35 Speyer and Sturmfels associated Gröbner toric degenerations Gr2(Cn)T of Gr2(Cn) taking an ideal I (e.g., the ideal cutting out X out of either affine space resp. projective W. M. Goldman, Complex hyperbolic geometry, Oxford Mathematical

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by F Luo Cited by 31 the hyperbolic metric is also established if the triangulation is isotopic to a totally geodesic hyperbolic cone metric associated to an ideal triangulation is locally determined by its cone to the degeneration of the hyperideal tetrahedra. This is

### Publications for Stephan Tillmann 2020 2019 2018 2017 2016

5 Mar 2020 Ideal points of character minimal ideal triangulations of cusped hyperbolic 3-manifolds. Journal of Degenerations of ideal hyperbolic.

### Shapes of polyhedra and triangulations of the sphere - EMIS

by WP Thurston 1998 Cited by 279 a hexagon can degenerate to an equilateral triangle. All dihedral angles of this hyperbolic polyhedron are π/2. Four edges meet at each ideal

### Incompressibility criteria for spun-normal surfaces - People

by NM DUNFIELD Cited by 33 variety defined by the hyperbolic gluing equations for T Theorem 1.1 is a strength- spun-normal surfaces in an ideal triangulation T arise from an ideal point of the Suppose ∆ is a non-degenerate ideal tetrahedron in H3 , which has an

### FROM VEERING TRIANGULATIONS TO PSEUDO-ANOSOV

25 Jun 2018 ideal triangulation T and a transverse veering structure α. Then there is a unique Degenerations of ideal hyperbolic triangulations. Mathema-.

### THE QUANTUM CONTENT OF THE GLUING EQUATIONS

by T DIMOFTE 2012 Cited by 71 It is well known that the set X of ideal triangulations of a cusped hyperbolic manifold is non-empty We call the tetrahedron non-degenerate if none of the

### Pacific Journal of Mathematics - NSF-PAR

by G Kuperberg 2019 Cited by 26 statement of the geometrization theorem, basic hyperbolic geometry, and old results from uses ideal triangulations of cusped 3-manifolds, together with Dehn fillings to However, f ( ) may be degenerate, meaning that it has zero volume, or.

### Valuations, Trees, and Degenerations of Hyperbolic - JSTOR

by JW Morgan 1984 Cited by 437 compactification of X whose ideal points are determined by valuations. All these actions have the property that the stabilizer of any non-degenerate arc is cyclic. S -* T. We may take f to be simplicial with respect to the given triangulation of.

### Singular pleated surfaces and CP1 structures - Cambridge

by SP Tan 1995 Cited by 2 If Fg has a hyperbolic structure then the triangulation can be made geometric, i.e., we can Let T(s1,s2,s3) be a non-degenerate hyperbolic triangle. Then structure are now ideal triangles so that the cone angle at the singular point is zero.

### A Combinatorial Curvature Flow for Ideal Triangulations

by Y Tianyu 2019 ideal triangulations with one or more hyperbolic ideal tetrahedra. lengths in L(T ), no tetrahedron can degenerate under the flow, in finite or infinite time.

### ON PARAMETERIZATIONS OF TEICHM¨ULLER SPACES OF

by R Guo Cited by 11 In a hyperbolic metric, any hexagon in an ideal triangulation is iso- topic (leaving the boundary of a Degenerations of a hyperbolic hexagon. In this section we

### The Volume Conjecture - Harvard Math

by S Lewallen 2008 6.3 Volume of Ideal Hyperbolic Tetrahedra 37 7.3 Degeneration into a triangulation of M = S3 − L combinatorics of a hyperbolic triangulation of the knot complement. The one thing we

### ON THE VOLUME AND THE CHERN-SIMONS INVARIANT

by JIY HAM and the formula for the complex volume of a hyperbolic knot in [3] to present explicit Neumann describe ̂β(M) directly in terms of an ideal triangulation Τ of M. By ing sure that the resulting ideal simplices are non-degenerate (all four

### Thurston's notes - William P. Thurston The Geometry and

by WP Thurston Cited by 1503 Any realization of T1, ,Tj as ideal hyperbolic tetrahedra determines a hyper- so that the two tetrahedra are non-degenerate and positively oriented. For each The link L of the single ideal vertex has a triangulation which can be calculated.

### Mathematisches Forschungsinstitut Oberwolfach Tropical

[18] Stephan Tillmann: Degenerations of ideal hyperbolic triangulations, arXiv:math/0508295v2. Floor decomposition of plane tropical curves and Caporaso-

### Triangulations, Heegaard splittings and hyperbolic geometry

20 Nov 2007 A. Positively oriented ideal hyperbolic tetrahedra are parametrized by the there exist a compact subset K of H such that any ideal triangulation of any cusped Annuli in generalized Heegaard splittings and degeneration.

### Note on Character Varieties and Cluster Algebras - Math-Net.Ru

by K Hikami 2019 Cited by 5 algebra associated with ideal triangulations of surfaces, and we show that originates from ideal triangulation of surfaces and was used [34] for hyperbolic algebra whose quiver is for a degeneration of ideal triangulation.

### Ideal triangulations of 3 manifolds II - Mathematical Sciences

by E Kang 2005 Cited by 17 existence of ideal triangulations admitting (complete) hyperbolic metrics. ples of taut ideal triangulations which do not admit an angle structure. [23] S Tillmann, Degenerations and normal surface theory, PhD thesis,

### 1304.6721 - Edinburgh Research Explorer - The University of

by TDD Gaiotto Cited by 53 These are ideal triangulations of C meaning that all edges in the tu,θ that is not the univalent edge in a degenerate triangle 13These are a natural generalization of Thurston's shear coordinates in 2d hyperbolic geometry, thereafter.

### PARTIALLY FLAT IDEAL TRIANGULATIONS OF - CORE

by C Petronio 2000 Cited by 30 Therefore if a manifold has a cusped finite-volume hyperbolic structure then it admits a degenerate geodesic ideal triangulation, in which some (but not all) of the

### On character varieties& Surfaces associated to Rutation W

are associated to degenerations of ideal triangulations of 3-manifolds. complete hyperbolic 3-manifold of finite volume with an ideal hyperbolic triangu - lation

### Research Statement

by T Yang Suppose the decorated hyperbolic surface Σ is ideally triangulated, and E is the set Euler characteristic and let T be an ideal triangulation of M. A hyperbolic cone degeneration of hyperideal tetrahedra, we show that the co-volume function

### arXiv:math/0508295v4 [math.GT] 7 Jun 2011

by S Tillmann 2005 Cited by 27 Degenerations of ideal hyperbolic triangulations Keywords 3 manifold, ideal triangulation, parameter space, character variety, detected

### Woods Hole Mathematics : Cell Decomposition and

§6 contains older work that explains the degeneration of hyperbolic struc- ture in our Fix an ideal triangulation r of Fg. Define a cycle of triangles (tj)™ to be a.

### Hyperbolic Knot Theory - BYU Math

by JS Purcell Cited by 12 Hyperbolic geometry and ideal tetrahedra. 19 The figure 8 knot has a topological ideal triangulation tom polyhedron after collapsing degenerate polyhedra.

### UNIVERSITY OF CALIFORNIA, SAN DIEGO - UCSD Math

by GP Hazel 2004 Cited by 9 degenerations of the metric) which appear as the flow evolves are directly related a spinal triangulation of F. It is a genuine hyperbolic triangulation in the case where B For a hyperbolic triangle with one ideal vertex, horocyclic coordinate.

### 3-Manifolds and 3d indices - Caltech Authors

by T Dimofte 2013 Cited by 281 2Mathematically, it is well known that hyperbolic 3-manifolds define elements in the defined by using any ideal triangulation of M, and it is invariant under 2 to 3 moves. Our [58] S. Tillmann, Degenerations of ideal hyperbolic triangulations,.

### A generalisation of the deformation variety - Project Euclid

by H Segerman 2012 Cited by 12 variety, even if the triangulation is minimal. The problem arises when the shape of an ideal hyperbolic tetrahedron would be degenerate, ie that

### RANDOM VEERING TRIANGULATIONS ARE NOT

by D FUTER 2019 Cited by 3 produce an ideal triangulation of ˚Mϕ (that is, a decomposition of ˚Mϕ into Every q P EQDppSq defines a doubly degenerate hyperbolic structure on Sˆ R, con-.

### Geometric transitions: from hyperbolic to AdS - UT Math

by J Danciger 2010 Cited by 22 setting in the case when an ideal triangulation is available. A degenerate H2 ideal tetrahedron is a hyperbolic tetrahedron with real shape

### Singular hyperbolic structures on pseudo-Anosov mapping tori

by K Kozai 2013 Cited by 4 prove some partial results on nearly collapsed ideal triangulations. vii smooth on the complement of Σ, that degenerate to a transversely hyperbolic foliation.

### REPRESENTATIONS VIA TRIANGULATIONS IN DIMENSION 2

are significant since many 3-manifolds admit hyperbolic structures, which In this note, we shall show how an ideal triangulation gives a parametrization of repre- and P. Shalen, Valuations, trees, and degenerations of hyperbolic structures.

### JHEP07(2018)145 - InSPIRE HEP

by D Ganga Cited by 33 S3,K] theory for all hyperbolic twist knots K has a surprising SU(3) symmetry. ideal triangulation of the knot complement M K. These two theories are argued In a degenerate limit when b → 0, which corresponds to the limit.

### ON IDEAL POINTS OF DEFORMATION CURVES OF

by T Yoshida 1991 Cited by 35 BY a hyperbolic 3-manifold we will mean an oriented complete hyperbolic Such a decomposition is called an ideal triangulation of N. Associated to an idcal trees and degenerations of hyperbolic structures, I. Ann. hfurh.

### Applications of Toric Geometry to 3-Manifold Triangulations

30 Jun 2014 triangulations, and to the introduction of cusped hyperbolic manifolds. In a fluent 2.1.2 Parameter equations of an ideal hyperbolic 3-simplex 21 between 0 and π, avoiding some possible degenerations. Although