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Constructing a covering triangulation by means of a nowhere-zero dual flow

1982
*
Journal of combinatorial theory. Series B (Print)
*

Tutte conjectured that every graph with no isthmus can be provided with an integral

doi:10.1016/0095-8956(82)90007-7
fatcat:273d45khmjerxoa74h5v5zwqii
*nowhere*-*zero**flow*with no absolute value greater than k = 5. ... G(" stands for the composition*of*G*by*an independent set*of*m vertices. ...*A*suficient condition for the existence*of**a**covering**triangulation*R verifving x1 = K:p, is the existence on K*of**a**nowhere*-*zero**dual**flow*with values in ZP. ...##
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A Simplicial Tutte "5"-flow Conjecture
[article]

2014
*
arXiv
*
pre-print

This paper concerns

arXiv:1409.6087v1
fatcat:qox33c6lebbt5ps75qf7lldj3m
*a*generalization*of**nowhere*-*zero*modular q-*flows*from graphs to simplicial complexes*of*dimension d greater than 1. ...*A*modular q-*flow**of**a*simplicial complex is an element*of*the kernel*of*the d-th boundary map with coefficients in Z/qZ; it is called*nowhere*-*zero*if it is not*zero*restricted to any*of*the facets*of*the ... Proof*of*Theorem 1.4.*By*Lemma 5.7, ∆ has coarboricity most c ≤ d + 2.*By*Lemma 5.4, ∆ has*a*2 c -*flow*. ...##
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Page 470 of Mathematical Reviews Vol. , Issue 84b
[page]

1984
*
Mathematical Reviews
*

Bouchet, André 84b:05043

*Constructing**a**covering**triangulation**by**means**of**a**nowhere*-*zero**dual**flow*. J. Combin. Theory Ser. B 32 (1982), no. 3, 316-325. ... Tutte that every graph with no isthmus admits an integral*nowhere*-*zero**flow*, with the maximum absolute value*of*the*flow*on any edge no greater than 5. ...##
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CAT(-1)-Type Properties for Teichmüller Space
[article]

2018
*
arXiv
*
pre-print

We show that if Teichm\"uller geodesics spend enough time in the thick part

arXiv:1808.10022v2
fatcat:wfkwfj6s3barvngk2qy4vfumka
*of*moduli space, they display CAT(-1)-type properties. ... There is*a*discrete set*of*times at which the*triangulation*changes, one*dual*train track splits along forward*flow*; the other splits along backward*flow*. ... Sketch*of*Proof One may associate*a*canonical choice*of**triangulation*to almost every point along almost every Teichmüller*flow*line, which is*dual*to*a*pair*of*train tracks. ...##
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Discrete holomorphic geometry I. Darboux transformations and spectral curves

2009
*
Journal für die Reine und Angewandte Mathematik
*

We propose an approach to discrete conformality that is based on the concept

doi:10.1515/crelle.2009.092
fatcat:45idlzatgzcpvhgycfe7qtvih4
*of*holomorphic line bundles over "discrete surfaces",*by*which we*mean*the vertex sets*of**triangulated*surfaces with bi-colored ... In the special case*of*maps into the 2-sphere we obtain*a*reinterpretation*of*the theory*of*complex holomorphic functions on discrete surfaces introduced*by*Dynnikov and Novikov. ... Similarly,*by*(universal)*covering**of**a*discrete surface M we*mean*the vertex set*of*the*triangulation*induced on*a**covering*(the universal*covering*)*of*the underlying smooth surface. ...##
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Problems in foliations and laminations of 3-manifolds

2002
*
arXiv
*
pre-print

This is

arXiv:math/0209081v1
fatcat:ba27dzi7irddnjicddb4uhufm4
*a*problem list in the theory*of*foliations and laminations*of*3-manifolds. ... The focus is on the relationship*of*foliations and laminations with other aspects*of*3-manifold topology, especially with the Thurston theory*of*geometric structures. ... (3) Kronheimer and Mrowka ( [75] ) found*a*characterization*of*the unit ball*of*the*dual*Thurston norm*by**means**of*differential geometry. ...##
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The Coherent-Constructible Correspondence and Homological Mirror Symmetry for Toric Varieties
[article]

2011
*
arXiv
*
pre-print

This is an expository article describing recent results

arXiv:0901.4276v2
fatcat:n5s2a63n3bgblhyhmesdri6ney
*of*the authors and David Nadler on microlocalization, the Fukaya category, and coherent sheaves on toric varieties. ... We recall what we*mean**by*the category*of**constructible*sheaves, Sh c (B). ... We then describe how, beginning with an equivariant ample line bundle on*a*toric variety X Σ*constructed*from*a*fan Σ ⊂ N R , we*construct**a*Lagrangian submanifold*of*the T-*dual*mirror geometry. ...##
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Quiver algebras as Fukaya categories

2015
*
Geometry and Topology
*

We embed

doi:10.2140/gt.2015.19.2557
fatcat:uwdpcbfydrcflgasdxpmyxljt4
*triangulated*categories defined*by*quivers with potential arising from ideal*triangulations**of*marked bordered surfaces into Fukaya categories*of*quasi-projective 3-folds associated to meromorphic ... Together with previous results, this yields non-trivial computations*of*spaces*of*stability conditions on Fukaya categories*of*symplectic 6-manifolds. ... There is*a**nowhere**zero*holomorphic volume form κ φ on Y φ . Proof. ...##
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Existence of unimodular triangulations - positive results
[article]

2017
*
arXiv
*
pre-print

We include, in particular, the first effective proof

arXiv:1405.1687v3
fatcat:izvgachey5aahayjct6lqubvmi
*of*the classical result*by*Knudsen-Mumford-Waterman stating that every lattice polytope has*a*dilation that admits*a*unimodular*triangulation*. ... In this article, we review several classes*of*polytopes that do have unimodular*triangulations*and*constructions*that preserve their existence. ...*A*very similar argument applies for polynomials counting*nowhere*-*zero**flows*or*nowhere*-*zero*tensions [23] and even for the Tutte polynomial*of**a*graph [24] . ...##
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Vector fields on polyhedra

1977
*
Transactions of the American Mathematical Society
*

One can show that there is

doi:10.1090/s0002-9947-1977-0451258-6
fatcat:4dgtwx3wobannprwsglrxrrehy
*a*correspondence between piecewise smooth*flows*on*a*polyhedron P and sections*of*the tangent object*of*P (i.e., vector fields on P); using this result one can prove existence ... This paper presents*a*bundle theory for studying vector fields and their integral*flows*on polyhedra^ and applications. ... The purpose*of*the following result is to show existence*of*piecewise smooth*flows*. 3.4. Proposition. Let T: X -* R" be*a**triangulation**of*R"*by**a*simplicial space X. ...##
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Subsurface distances for hyperbolic 3-manifolds fibering over the circle
[article]

2022
*
arXiv
*
pre-print

For

arXiv:2202.06883v1
fatcat:l3hbbfwt5ndhpo4i45qzbksdui
*a*hyperbolic fibered 3-manifold M, we prove results that uniformly relate the structure*of*surface projections as one varies the fibrations*of*M. ... Minsky was partially supported*by*NSF grants DMS-1610827 and DMS-2005328, and Taylor was partially supported*by*NSF grants DMS-1744551 and DMS-2102018 and the Sloan Foundation. ... Here, ∆ is an ideal*triangulation**of*X, which*by**construction*consists*of*τ -edges. We will also refer to the image*of*s in N , which we often denote*by*T , as*a*section. ...##
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Cohomology fractals, Cannon-Thurston maps, and the geodesic flow
[article]

2022
*
arXiv
*
pre-print

This allows us to verify our implementations

arXiv:2010.05840v2
fatcat:bbj24wwdhfht7g3ex5mrs5qwxq
*by*comparing our images*of*cohomology fractals to existing pictures*of*Cannon-Thurston maps. ... We discovered cohomology fractals while attempting to illustrate Cannon-Thurston maps without using vector graphics; we prove*a*correspondence between these two, when the cohomology class is*dual*to*a*... We thank Mark Pollicott and Alex Kontorovich for guiding us through the literature on exponential mixing*of*the geodesic*flow*. ...##
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On Computability and Triviality of Well Groups
[article]

2015
*
arXiv
*
pre-print

For the first part, we identify

arXiv:1501.03641v2
fatcat:zkfj7uirhnf6zakhdn2mq2gqdm
*a*computable subgroup*of*the well group that is obtained*by*cap product with the pullback*of*the orientation*of*R^n*by*f. ... We discuss on*a*possible replacement*of*the well groups*of*vector valued maps*by*an invariant*of**a*better descriptive power and computability status. ... This can be extended to*a**nowhere**zero*vector field in*a*neighborhood*of**A*and used to define*a*collar neighborhood*of**A*diffeomorphic to*A*× [0, ) for some > 0, the diffeomorphism induced*by*the*flow*...##
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Increasing the number of fibered faces of arithmetic hyperbolic 3-manifolds

2010
*
American Journal of Mathematics
*

More precisely, it has

doi:10.1353/ajm.0.0098
fatcat:c2l7ddiyrfapdbkeg3qywciycy
*a*tower*of*finite*covers*where the number*of*fibered faces*of*the Thurston norm ball goes to infinity, in fact faster than any power*of*the logarithm*of*the degree*of*the*cover*, ... We also give*a*non-compact finite-volume hyperbolic 3-manifold with the same properties*by*using*a*direct topological argument. ...*Constructing*X(Q). In order to build X(Q), we begin*by*claiming that it*covers*X ′ and that this*cover*X(Q) → X ′ is*a*cyclic*cover**of*degree 4. ...##
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Trivial Connections on Discrete Surfaces

2010
*
Computer graphics forum (Print)
*

This paper presents

doi:10.1111/j.1467-8659.2010.01761.x
fatcat:kmntadewunegfodvf2d2viswbq
*a*straightforward algorithm for*constructing*connections on discrete surfaces that are as smooth as possible everywhere but on*a*set*of*isolated singularities with given index. ... We compute these connections*by*solving*a*single linear system built from standard operators. ... This research was partially funded*by*NSF grants (CCF-0635112, CCF-0811373, CMMI-0757106, and CCF-1011944), the Center for the Mathematics*of*Information at Caltech, and the IAS at TU München. ...
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