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

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 Equivariant Map Queer Lie Superalgebras

2016 ◽  
Vol 68 (2) ◽  
pp. 258-279 ◽  
Author(s):  
Lucas Calixto ◽  
Adriano Moura ◽  
Alistair Savage
Keyword(s):  
Finite Group ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Equivariant Map ◽  
Isomorphism Classes ◽  
Finite Dimensional ◽  
Regular Maps ◽  
A Finite Group ◽  
Special Case

AbstractAn equivariant map queer Lie superalgebra is the Lie superalgebra of regular maps from an algebraic variety (or scheme) X to a queer Lie superalgebra q that are equivariant with respect to the action of a finite group Γ acting on X and q. In this paper, we classify all irreducible finite-dimensional representations of the equivariant map queer Lie superalgebras under the assumption that Γ is abelian and acts freely on X. We show that such representations are parameterized by a certain set of Γ-equivariant finitely supported maps from X to the set of isomorphism classes of irreducible finite-dimensional representations of q. In the special case where X is the torus, we obtain a classification of the irreducible finite-dimensional representations of the twisted loop queer superalgebra.

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.

Periods for Continuous Self-Maps of the Figure-Eight Space

2003 ◽  
Vol 13 (07) ◽  
pp. 1743-1754 ◽  
Author(s):  
Jaume Llibre ◽  
José Paraños ◽  
J. Ángel Rodríguez
Keyword(s):  
Euler Characteristic ◽  
Connected Graph ◽  
Complete Classification ◽  
Branching Points ◽  
Branching Point

Let 8 be the graph shaped like the number 8. This paper contains a characterization of all possible sets of periods for all continuous self-maps of 8 with the branching point fixed. We remark that this characterization is the first complete classification of the sets of periods for all continuous self-maps on a connected graph with negative Euler characteristic with fixed branching points.

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