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

André Bouchet
1982 Journal of combinatorial theory. Series B (Print)  
Tutte conjectured that every graph with no isthmus can be provided with an integral 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.  ... 
doi:10.1016/0095-8956(82)90007-7 fatcat:273d45khmjerxoa74h5v5zwqii

A Simplicial Tutte "5"-flow Conjecture [article]

Bradley Lewis Burdick
2014 arXiv   pre-print
This paper concerns 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.  ... 
arXiv:1409.6087v1 fatcat:qox33c6lebbt5ps75qf7lldj3m

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.  ... 

CAT(-1)-Type Properties for Teichmüller Space [article]

Ian Frankel
2018 arXiv   pre-print
We show that if Teichm\"uller geodesics spend enough time in the thick part 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.  ... 
arXiv:1808.10022v2 fatcat:wfkwfj6s3barvngk2qy4vfumka

Discrete holomorphic geometry I. Darboux transformations and spectral curves

C. Bohle, F. Pedit, U. Pinkall
2009 Journal für die Reine und Angewandte Mathematik  
We propose an approach to discrete conformality that is based on the concept 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.  ... 
doi:10.1515/crelle.2009.092 fatcat:45idlzatgzcpvhgycfe7qtvih4

Problems in foliations and laminations of 3-manifolds

Danny Calegari
2002 arXiv   pre-print
This is 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.  ... 
arXiv:math/0209081v1 fatcat:ba27dzi7irddnjicddb4uhufm4

The Coherent-Constructible Correspondence and Homological Mirror Symmetry for Toric Varieties [article]

Bohan Fang, Chiu-Chu Melissa Liu, David Treumann, Eric Zaslow
2011 arXiv   pre-print
This is an expository article describing recent results 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.  ... 
arXiv:0901.4276v2 fatcat:n5s2a63n3bgblhyhmesdri6ney

Quiver algebras as Fukaya categories

Ivan Smith
2015 Geometry and Topology  
We embed 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.  ... 
doi:10.2140/gt.2015.19.2557 fatcat:uwdpcbfydrcflgasdxpmyxljt4

Existence of unimodular triangulations - positive results [article]

Christian Haase, Andreas Paffenholz, Lindsay C. Piechnik, Francisco Santos
2017 arXiv   pre-print
We include, in particular, the first effective proof 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] .  ... 
arXiv:1405.1687v3 fatcat:izvgachey5aahayjct6lqubvmi

Vector fields on polyhedra

Michael A. Penna
1977 Transactions of the American Mathematical Society  
One can show that there is 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.  ... 
doi:10.1090/s0002-9947-1977-0451258-6 fatcat:4dgtwx3wobannprwsglrxrrehy

Subsurface distances for hyperbolic 3-manifolds fibering over the circle [article]

Yair N. Minsky, Samuel J. Taylor
2022 arXiv   pre-print
For 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.  ... 
arXiv:2202.06883v1 fatcat:l3hbbfwt5ndhpo4i45qzbksdui

Cohomology fractals, Cannon-Thurston maps, and the geodesic flow [article]

David Bachman, Matthias Goerner, Saul Schleimer, Henry Segerman
2022 arXiv   pre-print
This allows us to verify our implementations 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.  ... 
arXiv:2010.05840v2 fatcat:bbj24wwdhfht7g3ex5mrs5qwxq

On Computability and Triviality of Well Groups [article]

Peter Franek, Marek Krcal
2015 arXiv   pre-print
For the first part, we identify 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  ... 
arXiv:1501.03641v2 fatcat:zkfj7uirhnf6zakhdn2mq2gqdm

Increasing the number of fibered faces of arithmetic hyperbolic 3-manifolds

Nathan M. Dunfield, Dinakar Ramakrishnan
2010 American Journal of Mathematics  
More precisely, it has 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.  ... 
doi:10.1353/ajm.0.0098 fatcat:c2l7ddiyrfapdbkeg3qywciycy

Trivial Connections on Discrete Surfaces

Keenan Crane, Mathieu Desbrun, Peter Schröder
2010 Computer graphics forum (Print)  
This paper presents 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.  ... 
doi:10.1111/j.1467-8659.2010.01761.x fatcat:kmntadewunegfodvf2d2viswbq
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