Big pure mapping class groups are never perfect
نویسندگان
چکیده
We show that the closure of compactly supported mapping class group an infinite type surface is not perfect and its abelianization contains a direct summand isomorphic to uncountable sum rationals. also extend this Torelli in case surfaces with genus indivisible copy free abelian as well. Finally we give application question automatic continuity by exhibiting discontinuous homomorphisms
منابع مشابه
On the Lie Algebras Associated with Pure Mapping Class Groups
Mapping class group is an important object in Topology, Complex Analysis, Algebraic Geometry and other domains. It is a lucky case when the method of Algebraic Topology works perfectly well, the application of the functor of fundamental group completely solves the topological problem: group of isotopy classes of homeomorphisms is described in terms of automorphisms of the fundamental group of t...
متن کامل2 Mapping Class Groups Are Not Kähler
The goal of these notes is to prove that the mapping class groups of a closed orientable surface of genus two, with punctures, are not Kähler
متن کاملCountable Groups Are Mapping Class Groups of Hyperbolic 3-manifolds
We prove that for every countable group G there exists a hyperbolic 3-manifold M such that the isometry group of M , the mapping class group of M , and the outer automorphism group of π1(M) are isomorphic to G.
متن کاملThe Center of Some Braid Groups and the Farrell Cohomology of Certain Pure Mapping Class Groups
In this paper we first show that many braid groups of low genus surfaces have their centers as direct factors. We then give a description of centralizers and normalizers of prime order elements in pure mapping class groups of surfaces with spherical quotients using automorphism groups of fundamental groups of the quotient surfaces. As an application, we use these to show that the p-primary part...
متن کاملPerfect Mclain Groups Are Superperfect
The study of McLain groups M(S, F) offers an attractive interplay between group theory and combinatorial set theory. This arises from the choice of a linearly ordered set S in the definition. Recall (from, for example, [4], (6.2)) that this involves considering the vector space V over the field F whose basis elements v are indexed by elements of x S . M(S, F) is then the group of linear transfo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2022
ISSN: ['1073-2780', '1945-001X']
DOI: https://doi.org/10.4310/mrl.2022.v29.n3.a4