Finite quotients of symplectic groups vs mapping class groups

Details Finite quotients of symplectic groups vs mapping class groups Finite quotients of symplectic groups vs mapping class groups

2011-03-09

arxiv.org/abs/1103.1855v1

Mathematics

Geometric Topology

19p

Scientific paper

We prove that the essential 2-homology of finite quotients of symplectic groups over a fixed Dedekind domain of arithmetic type are torsion groups of uniformly bounded size. This is shown to be equivalent to a result of Deligne proving that suitable central extensions of higher rank Chevalley groups over Dedekind domains of arithmetic type are not residually finite. Using this equivalence one improves Deligne's non-residually finiteness result by showing that homomorphisms of the universal central extension of $Sp(2g,\Z)$ to finite groups factor through $Sp(2g,\Z)$, when $g\geq 3$. Furthermore, one proves that, for every prime $p\geq 5$, the mapping class group of genus $g\geq 3$ has finite quotients whose essential 2-homology has $p$-torsion. This is a simple consequence of the existence of quantum representations.

Affiliated with

Also associated with

No associations

Rating

Finite quotients of symplectic groups vs mapping class groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Finite quotients of symplectic groups vs mapping class groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite quotients of symplectic groups vs mapping class groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-645094