0000000001085770

AUTHOR

A. J. Berrick

showing 1 related works from this author

Finite index subgroups of mapping class groups

2011

Let g ≥ 3 and n ≥ 0, and let Mg,n be the mapping class group of a surface of genus g with n boundary components. We prove that Mg,n contains a unique subgroup of index 2g−1(2g − 1) up to conjugation, a unique subgroup of index 2g−1(2g + 1) up to conjugation, and the other proper subgroups ofMg,n are of index greater than 2g−1(2g+1). In particular, the minimum index for a proper subgroup of Mg,n is 2g−1(2g − 1). AMS Subject Classification. Primary: 57M99. Secondary: 20G40, 20E28. 0 Introduction and statement of results The interaction between mapping class groups and finite groups has long been a topic of interest. The famous Hurwitz bound of 1893 showed that the mapping class group of a clo…

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT][ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]General MathematicsGroup Theory (math.GR)01 natural sciencesUpper and lower bounds[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]CombinatoricsMathematics - Geometric Topologysymbols.namesake57M99SubgroupGenus (mathematics)[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesFOS: MathematicsOrder (group theory)0101 mathematicsQuotientMathematicsRiemann surface010102 general mathematicsGeometric Topology (math.GT)Mapping class groupOrientation (vector space)symbols010307 mathematical physicsMathematics - Group Theory
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