Profinite mapping class groups

2018/12/13 by Igor Nikolaev, Nikolaev, Igor · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1812.05390

Abstract

It is proved that the profinite completion of the mapping class group Mod (g,n) of a surface of genus g with n boundary components is isomorphic to such of the arithmetic group GL(6g-6+2n, Z). We establish a relation between the normal subgroups of Mod (g,n) and the absolute Galois group G(K) of a number field K. Using the Tits alternative, we prove the Shafarevich Conjecture saying that the group G(Q^ab) of the maximal abelian extension of the field of rationals is isomorphic to a free profinite group.

Cited by

• Arithmetic topology of 4-manifolds

Related

• Groups of profinite type and profinite rigidity
• On function fields with free absolute Galois groups
• Big pure mapping class groups are never perfect
• Relative Pro-ℓ Completions of Mapping Class Groups
• Algebro-geometric subgroups of mapping class groups