NDLI: Congruence Veech groups

Content Provider	Springer Nature Link
Author	Finster, Myriam
Copyright Year	2016
Abstract	We study Veech groups of covering surfaces of primitive translation surfaces. Therefore we define congruence subgroups in Veech groups of primitive translation surfaces using their action on the homology with entries in Z/aZ. We introduce a congruence level definition and a property of a primitive translation surface which we call property (★). It guarantees that partition stabilising congruence subgroups of this level occur as Veech groups of a translation covering.Each primitive surface with exactly one singular point has property (★) in every level. We additionally show that the surface glued from a regular 2n-gon with odd n has property (★) in level a iff a and n are coprime. For the primitive translation surface glued from two regular n-gons, where n is an odd number, we introduce a generalised Wohlfahrt level of subgroups in its Veech group. We determine the relationship between this Wohlfahrt level and the congruence level of a congruence group.
Starting Page	885
Ending Page	930
Page Count	46
File Format	PDF
ISSN	00212172
Journal	Israel Journal of Mathematics
Volume Number	214
Issue Number	2
e-ISSN	15658511
Language	English
Publisher	The Hebrew University Magnes Press
Publisher Date	2016-09-07
Publisher Place	Jerusalem
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematics Algebra Group Theory and Generalizations Analysis Applications of Mathematics Theoretical, Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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