Almost-regular Dessins d'Enfant on a torus and sphere

Joachim König; Arielle Leitner; Danny Neftin

doi:10.1016/j.topol.2018.05.002

Almost-regular Dessins d'Enfant on a torus and sphere

Joachim König
, Arielle Leitner
, Danny Neftin

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

The Hurwitz problem asks which ramification data are realizable, i.e., appear as the ramification type of a covering. We use dessins d'enfant to show that families of genus 1 regular ramification data with small changes are realizable with the exception of four families which were recently shown to be nonrealizable. A similar description holds in the case of genus 0 ramification data.

Original language	English
Pages (from-to)	78-99
Number of pages	22
Journal	Topology and its Applications
Volume	243
DOIs	https://doi.org/10.1016/j.topol.2018.05.002
State	Published - 1 Jul 2018

Keywords

Branched coverings
Dessin's d'Enfants
Regular maps
Tilings

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1016/j.topol.2018.05.002

Cite this

@article{6da2c64535e746328c4fc8d033a57e34,

title = "Almost-regular Dessins d'Enfant on a torus and sphere",

abstract = "The Hurwitz problem asks which ramification data are realizable, i.e., appear as the ramification type of a covering. We use dessins d'enfant to show that families of genus 1 regular ramification data with small changes are realizable with the exception of four families which were recently shown to be nonrealizable. A similar description holds in the case of genus 0 ramification data.",

keywords = "Branched coverings, Dessin's d'Enfants, Regular maps, Tilings",

author = "Joachim K{\"o}nig and Arielle Leitner and Danny Neftin",

note = "Funding Information: We thank Nir Lazorovich for the help in proving Lemma 3.4 and Konstantin Golubyev for helpful discussions. We thank Michael Zieve for introducing the composition obstruction used in Conjecture 6.3 , and other helpful discussions. This work is partially supported by the Israel Science Foundation (grant No. 577/15 ) and the United States-Israel Binational Science Foundation (grant No. 2014173 ). The second author thanks the ISF-UGC joint research program framework grant No. 1469/14 . Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2018",

month = jul,

day = "1",

doi = "10.1016/j.topol.2018.05.002",

language = "English",

volume = "243",

pages = "78--99",

journal = "Topology and its Applications",

issn = "0166-8641",

publisher = "Elsevier BV",

}

TY - JOUR

T1 - Almost-regular Dessins d'Enfant on a torus and sphere

AU - König, Joachim

AU - Leitner, Arielle

AU - Neftin, Danny

N1 - Funding Information: We thank Nir Lazorovich for the help in proving Lemma 3.4 and Konstantin Golubyev for helpful discussions. We thank Michael Zieve for introducing the composition obstruction used in Conjecture 6.3 , and other helpful discussions. This work is partially supported by the Israel Science Foundation (grant No. 577/15 ) and the United States-Israel Binational Science Foundation (grant No. 2014173 ). The second author thanks the ISF-UGC joint research program framework grant No. 1469/14 . Publisher Copyright: © 2018 Elsevier B.V.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - The Hurwitz problem asks which ramification data are realizable, i.e., appear as the ramification type of a covering. We use dessins d'enfant to show that families of genus 1 regular ramification data with small changes are realizable with the exception of four families which were recently shown to be nonrealizable. A similar description holds in the case of genus 0 ramification data.

AB - The Hurwitz problem asks which ramification data are realizable, i.e., appear as the ramification type of a covering. We use dessins d'enfant to show that families of genus 1 regular ramification data with small changes are realizable with the exception of four families which were recently shown to be nonrealizable. A similar description holds in the case of genus 0 ramification data.

KW - Branched coverings

KW - Dessin's d'Enfants

KW - Regular maps

KW - Tilings

UR - https://www.scopus.com/pages/publications/85047275215

U2 - 10.1016/j.topol.2018.05.002

DO - 10.1016/j.topol.2018.05.002

M3 - Article

SN - 0166-8641

VL - 243

SP - 78

EP - 99

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Almost-regular Dessins d'Enfant on a torus and sphere

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this