Profinite completions of Burnside-type quotients of surface groups

Abstract

Using quantum representations of mapping class groups we prove that profinite completions of Burnside-type surface group quotients are not virtually prosolvable, in general. Further, we construct infinitely many finite simple characteristic quotients of surface groups.

arXiv commentrevised version, 17p

References in corpus (12)

• The two-eigenvalue problem and density of Jones representation of braid groups
• Finite covers of random 3-manifolds
• Integral Lattices in TQFT
• Surjectivity Criteria for p-adic Representations, Part I
• Quantum SU(2) faithfully detects mapping class groups modulo center
• Quotients of surface groups and homology of finite covers via quantum representations
• Density of the SO(3) TQFT representation of mapping class groups
• Finite quotients of symplectic groups vs mapping class groups
• All finite groups are involved in the Mapping Class Group
• Quantum invariants of random 3-manifolds
• Some asymptotics of TQFT via skein theory
• Irreducible factors of modular representations of mapping class groups arising in Integral TQFT

Cited by in corpus (1)

• Quotients of the mapping class group by power subgroups