NDLI: Chirality groups of maps and hypermaps

Content Provider	Springer Nature Link
Author	Škoviera, Martin Breda D’Azevedo, Antonio Nedela, Roman Jones, Gareth
Copyright Year	2008
Abstract	Although the phenomenon of chirality appears in many investigations of maps and hypermaps, no detailed study of chirality seems to have been carried out. Chirality of maps and hypermaps is not merely a binary invariant but can be quantified by two new invariants—the chirality group and the chirality index, the latter being the size of the chirality group. A detailed investigation of the chirality groups of orientably regular maps and hypermaps will be the main objective of this paper. The most extreme type of chirality arises when the chirality group coincides with the monodromy group. Such hypermaps are called totally chiral. Examples of these are constructed by considering appropriate “asymmetric” pairs of generators of certain non-abelian simple groups. We also show that every finite abelian group is the chirality group of some hypermap, whereas many non-abelian groups, including symmetric and dihedral groups, cannot arise as chirality groups.
Ending Page	355
Page Count	19
Starting Page	337
File Format	PDF
ISSN	09259899
e-ISSN	15729192
Journal	Journal of Algebraic Combinatorics
Issue Number	3
Volume Number	29
Language	English
Publisher	Springer US
Publisher Date	2008-05-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Chirality index Finite automorphism groups of algebraic, geometric, or combinatorial structures Chiral Asymmetric Planar graphs; geometric and topological aspects of graph theory Graphs and abstract algebra (groups, rings, fields, etc.) Convex and Discrete Geometry Computer Science Hypermap Group Theory and Generalizations Order, Lattices, Ordered Algebraic Structures Combinatorics Map Chirality group
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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