scholarly journals Corrigendum to “Orientably-regular maps of Euler characteristic −2p2” [European J. Combin. 96 (2021) 103366]

2021 ◽  
pp. 103472
Author(s):  
Jicheng Ma
Keyword(s):  
Euler Characteristic ◽  
Regular Maps

scholarly journals Classification of regular maps of negative prime Euler characteristic

2004 ◽  
Vol 357 (10) ◽  
pp. 4175-4190 ◽  
Author(s):  
Antonio Breda d’Azevedo ◽  
Roman Nedela ◽  
Jozef Širáň
Keyword(s):  
Euler Characteristic ◽  
Regular Maps

scholarly journals Introducing edge-biregular maps

2021 ◽  
Author(s):  
Olivia Reade
Keyword(s):  
Automorphism Group ◽  
Euler Characteristic ◽  
Dihedral Group ◽  
Automorphism Groups ◽  
Triangle Group ◽  
Supporting Surface ◽  
Regular Maps ◽  
Special Cases ◽  
Edge Colourings

AbstractWe introduce the concept of alternate-edge-colourings for maps and study highly symmetric examples of such maps. Edge-biregular maps of type (k, l) occur as smooth normal quotients of a particular index two subgroup of $$T_{k,l}$$ T k , l , the full triangle group describing regular plane (k, l)-tessellations. The resulting colour-preserving automorphism groups can be generated by four involutions. We explore special cases when the usual four generators are not distinct involutions, with constructions relating these maps to fully regular maps. We classify edge-biregular maps when the supporting surface has non-negative Euler characteristic, and edge-biregular maps on arbitrary surfaces when the colour-preserving automorphism group is isomorphic to a dihedral group.

scholarly journals Classification of regular maps of Euler characteristic −3p

2012 ◽  
Vol 102 (4) ◽  
pp. 967-981 ◽  
Author(s):  
Marston Conder ◽  
Roman Nedela ◽  
Jozef Širáň
Keyword(s):  
Euler Characteristic ◽  
Regular Maps

Enumeration of rooted 4-regular maps without planar loops

2021 ◽  
Vol 344 (8) ◽  
pp. 112442
Author(s):  
Evgeniy Krasko ◽  
Alexander Omelchenko
Keyword(s):  
Regular Maps

scholarly journals Vortices over Riemann surfaces and dominated splittings

2021 ◽  
pp. 1-26
Author(s):  
THOMAS METTLER ◽  
GABRIEL P. PATERNAIN
Keyword(s):  
Euler Characteristic ◽  
Tangent Bundle ◽  
Riemann Surfaces ◽  
Dominated Splitting ◽  
Vortex Equations ◽  
Special Cases ◽  
Unit Tangent Bundle ◽  
Anosov Flows

Abstract We associate a flow $\phi $ with a solution of the vortex equations on a closed oriented Riemannian 2-manifold $(M,g)$ of negative Euler characteristic and investigate its properties. We show that $\phi $ always admits a dominated splitting and identify special cases in which $\phi $ is Anosov. In particular, starting from holomorphic differentials of fractional degree, we produce novel examples of Anosov flows on suitable roots of the unit tangent bundle of $(M,g)$ .

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