Stable subgroups and Morse subgroups in mapping class groups
نویسندگان
چکیده
منابع مشابه
Convex cocompact subgroups of mapping class groups
We develop a theory of convex cocompact subgroups of the mapping class group MCG of a closed, oriented surface S of genus at least 2, in terms of the action on Teichmüller space. Given a subgroup G of MCG de ning an extension 1 ! 1(S) ! ΓG ! G ! 1, we prove that if ΓG is a word hyperbolic group then G is a convex cocompact subgroup of MCG. When G is free and convex cocompact, called a Schottky ...
متن کاملFinite index subgroups of mapping class groups
Let g ≥ 3 and n ≥ 0, and let Mg,n be the mapping class group of a surface of genus g with n boundary components. We prove that Mg,n contains a unique subgroup of index 2g−1(2g − 1) up to conjugation, a unique subgroup of index 2g−1(2g + 1) up to conjugation, and the other proper subgroups ofMg,n are of index greater than 2g−1(2g+1). In particular, the minimum index for a proper subgroup of Mg,n...
متن کاملOne-ended subgroups of mapping class groups
Let Σ be a closed orientable surface, and write Map(Σ) for its mapping class group — the group of self-homeomorphisms up to homotopy. The Nielsen-Thurston classification partitions the non-trivial elements of Map(Σ) into finite order, reducible, and pseudoanosov, the last being the “generic” case. A subgroup of Map(Σ) is purely pseudoanosov if every non-trivial element is pseudoanosov. Such a s...
متن کاملSurface subgroups of Mapping Class groups
Mod(Σ) = Homeo(Σ)/Homeo0(Σ), where, Homeo(Σ) is the group of orientation preserving homeomorphisms of Σ and Homeo0(Σ) are those homeomorphisms isotopic to the identity. When Σ is a closed surface of genus g ≥ 1 then we denote Mod(Σ) by Γg. In this case it is well-known that Γg is isomorphic to a subgroup of index 2 in Out(π1(Σ)). When g = 1, the subgroup structure of Γ1 is well-understood since...
متن کاملSeparable subgroups of mapping class groups
We investigate the separability of several well known classes of subgroups of the mapping class group of a surface.
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: International Journal of Algebra and Computation
سال: 2019
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196719500346