Injectivity radius of representations of triangle groups and planar width of regular hypermaps

Martin Mačaj, Jozef Širáň, Mária Ipolyiová

Abstract


 We develop a rigorous algebraic background for representations of triangle groups in linear groups over algebras arising from factor rings of multivariate polynomial rings. This is then used to substantially improve the existing upper bounds on the order of epimorphic images of triangle groups with a given injectivity radius and, analogously, the size of the associated hypermaps of a given type with a given planar width.

 


Keywords


triangle group; epimorphism; injectivity radius; regular hypermap; planar width

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DOI: https://doi.org/10.26493/1855-3974.50.b13

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications