Journal ArticleDOI
Graphs of stable maps between closed orientable surfaces
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In this article, the relationship between weighted graphs and stable maps between closed orientable surfaces was studied as a global invariant and as a tool for building maps between surfaces, and it was extended to the case of stable maps from closed orientedable surfaces to the 2-sphere.Abstract:
We study the relationship between weighted graphs and stable maps between closed orientable surfaces as a global invariant and as a tool for building maps between surfaces. This work extends our previous results for the case of stable maps from closed orientable surfaces to the 2-sphere.read more
Citations
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Journal ArticleDOI
On the periods of a continuous self-map on a graph
TL;DR: In this paper, the periods of the periodic orbits of a self-map on a graph were studied from another point of view, using either the action of the self map on its homology, or the shape of the graph G.
Journal ArticleDOI
Realization of graphs by fold Gauss maps
TL;DR: In this paper, it was shown that any 2-negative bipartite graph with total weight equal to zero can be associated with some fold Gauss map from a closed orientable surface.
Journal ArticleDOI
Eliashberg's $h$-principle and generic maps of surfaces with prescribed singular locus
TL;DR: In this article, the authors extend Eliashberg's h-principle to smooth maps of surfaces which are allowed to have cusp singularities, as well as folds, and prove a necessary and sufficient condition for a given map of surfaces to be homotopic to one with given loci of folds and cusps.
Journal ArticleDOI
Topological entropy of continuous self-maps on a graph
TL;DR: The second author is partially supported by the Ministerio de Economia, Industria y Competitividad, Agencia Estatal de Investigacion grants MTM-2016-77278-P (FEDER) and MDM-2014-0445, the Agencia de Gestio d’Ajuts Universitaris i de Recerca grant 2017SGR1617, and the H2020 European Research Council grant MSCA-RISE-2017-777911.
Posted Content
Eliashberg's $h$-principle and generic maps of surfaces with prescribed singular locus
TL;DR: In this article, the authors extend Eliashberg's $h$-principle to smooth maps of surfaces which are allowed to have cusp singularities, as well as folds, and prove a necessary and sufficient condition for a given map of surfaces to be homotopic to one with given loci of folds and cusps.
References
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Book ChapterDOI
On Singularities of Mappings of Euclidean Spaces. I. Mappings of the Plane Into the Plane
TL;DR: In this article, the authors consider all mappings f which are sufficiently good approximations to f 0 and show that if f 0 is r-smooth (i.e., has continuous partial derivatives of orders ≦r), r finite, then f 0 can be approximated by f 0.
Book
Complements of Discriminants of Smooth Maps: Topology and Applications
TL;DR: Cohomology of braid groups and configuration spaces of real functions without complicated singularities has been studied in the context of algebraic functions and interpolation theory by as discussed by the authors.
Journal ArticleDOI
First order local invariants of apparent contours
Toru Ohmoto,Francesca Aicardi +1 more
TL;DR: In this paper, first order local Vassiliev-type invariants of generic apparent contours are studied for a smooth map from a closed surface to the two-dimensional plane.
Journal ArticleDOI
A global theorem for singularities of maps between oriented 2-manifolds
TL;DR: The Riemann-Hurwitz formula of complex analysis has been generalized in this paper to the case of smooth compact oriented connected 2-manifolds, where the Euler characteristic and the topological degree at the cusp pointy are assumed to be the same.
Journal ArticleDOI
Stable maps from surfaces to the plane with prescribed branching data
TL;DR: In this paper, the authors consider the problem of constructing stable maps from surfaces to the plane with branch set a given set of curves immersed (except possibly with cusps) in the plane.