# The genera, reflexibility and simplicity of regular maps

Marston Conder; Jozef Širáň; Thomas Tucker

Journal of the European Mathematical Society (2010)

- Volume: 012, Issue: 2, page 343-364
- ISSN: 1435-9855

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topConder, Marston, Širáň, Jozef, and Tucker, Thomas. "The genera, reflexibility and simplicity of regular maps." Journal of the European Mathematical Society 012.2 (2010): 343-364. <http://eudml.org/doc/277173>.

@article{Conder2010,

abstract = {This paper uses combinatorial group theory to help answer some long-standing questions about the genera of orientable surfaces that carry particular kinds of regular maps. By classifying all orientably-regular maps whose automorphism group has order coprime to $g-1$, where $g$ is the genus, all orientably-regular maps of genus $p+1$ for $p$ prime are determined. As a consequence, it is shown that orientable surfaces of infinitely many genera carry no regular map that is chiral (irreflexible), and that orientable surfaces of infinitely many genera carry no reflexible regular map with simple underlying graph. Another consequence is a simpler proof of the Breda–Nedela–Širáň classification of non-orientable regular maps of Euler characteristic $-p$ where $p$ is prime.},

author = {Conder, Marston, Širáň, Jozef, Tucker, Thomas},

journal = {Journal of the European Mathematical Society},

keywords = {regular map; symmetric graph; embedding; genus; chiral; reflexible; regular map; symmetric graph; embedding; genus; chiral; reflexible},

language = {eng},

number = {2},

pages = {343-364},

publisher = {European Mathematical Society Publishing House},

title = {The genera, reflexibility and simplicity of regular maps},

url = {http://eudml.org/doc/277173},

volume = {012},

year = {2010},

}

TY - JOUR

AU - Conder, Marston

AU - Širáň, Jozef

AU - Tucker, Thomas

TI - The genera, reflexibility and simplicity of regular maps

JO - Journal of the European Mathematical Society

PY - 2010

PB - European Mathematical Society Publishing House

VL - 012

IS - 2

SP - 343

EP - 364

AB - This paper uses combinatorial group theory to help answer some long-standing questions about the genera of orientable surfaces that carry particular kinds of regular maps. By classifying all orientably-regular maps whose automorphism group has order coprime to $g-1$, where $g$ is the genus, all orientably-regular maps of genus $p+1$ for $p$ prime are determined. As a consequence, it is shown that orientable surfaces of infinitely many genera carry no regular map that is chiral (irreflexible), and that orientable surfaces of infinitely many genera carry no reflexible regular map with simple underlying graph. Another consequence is a simpler proof of the Breda–Nedela–Širáň classification of non-orientable regular maps of Euler characteristic $-p$ where $p$ is prime.

LA - eng

KW - regular map; symmetric graph; embedding; genus; chiral; reflexible; regular map; symmetric graph; embedding; genus; chiral; reflexible

UR - http://eudml.org/doc/277173

ER -

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