Arithmetic quotients of the mapping class group

作者：Grunewald Fritz^*; Larsen Michael; Lubotzky Alexander; Malestein Justin

来源：Geometric and Functional Analysis, 2015, 25(5): 1493-1542.

DOI：10.1007/s00039-015-0352-5

To every -irreducible representation r of a finite group H, there corresponds a simple factor A of with an involution . To this pair , we associate an arithmetic group consisting of all matrices over a natural order of which preserve a natural skew-Hermitian sesquilinear form on . We show that if H is generated by less than g elements, then is a virtual quotient of the mapping class group , i.e. a finite index subgroup of is a quotient of a finite index subgroup of . This shows that has a rich family of arithmetic quotients (and "Torelli subgroups") for which the classical quotient is just a first case in a list, the case corresponding to the trivial group H and the trivial representation. Other pairs of H and r give rise to many new arithmetic quotients of which are defined over various (subfields of) cyclotomic fields and are of type and for arbitrarily large m.

• 出版日期2015-10