相关论文: Separable subgroups of mapping class groups

We give a finite presentation of the mapping class group of an oriented (possibly bounded) surface of genus greater or equal than 1, considering Dehn twists on a very simple set of curves.

By recognizing them as fundamental groups of developable complexes of groups we prove that mapping class groups of compact orientable surfaces have finite asymptotic dimension.

We show that the automorphism group of the complex of pants decompositions for a surface is isomorphic to the mapping class group for that surface.

It is shown that various questions about the existence of simple closed curves in normal subgroups of surface groups are undecidable.

Let G be a finitely generated linear group over a field of characteristic 0. Suppose that every solvable subgroup of G is polycyclic. Then the claim is made that any solvable subgroup of G is separable. This is proven for G=SL_n(Z).…

We use fine curve graph tools to prove that there exist parabolic isometries of graphs of curves associated to surfaces of infinite type.

This paper completely determines the non-amenability of the mapping class groups of infinite-type surfaces, the mapping class groups of locally finite infinite graphs of higher ranks, gives an example of non-amenable stabiliser of a point…

We compute the invariant subspace of the rational group ring of a surface, truncated by powers of the augmentation ideal, under the action of the mapping class group. The surface is compact, oriented with one boundary component. This…

We describe the subgroup of the mapping class group of a hypersurface in $\mathbb{CP}^4$ consisting of those diffeomorphisms which can be realised by monodromy.

We compute the topological mapping class group of every compact, simply connected, topological 4-manifold. This was previously only known in the closed case. If the 4-manifold is smooth, we deduce an analogous description of the stable…

In this paper, we define the notion of a mapping on soft classes and study several properties of images and inverse images of soft sets supported by examples and counterexamples. Finally, these notions have been applied to the problem of…

We study the large-scale geometry of mapping class groups of surfaces of infinite type, using the framework of Rosendal for coarse geometry of non locally compact groups. We give a complete classification of those surfaces whose mapping…

A class of subgroups is obtained for symmetric groups using signed Brauer diagrams.

In this paper, we show that unswitchable graphs are a proper subclass of split graphs, and exploit this fact to propose efficient algorithms for their recognition and generation.

We present a comprehensive survey on removability of compact plane sets with respect to various classes of holomorphic functions. We also discuss some applications and several open questions, some of which are new.

Separability is one of the most basic and important topological properties. In this paper, the separability in (strongly) topological gyrogroups is studied. It is proved that every first-countable left {\omega}-narrow strongly topological…

Beauville surfaces are a class of complex surfaces defined by letting a finite group $G$ act on a product of Riemann surfaces. These surfaces possess many attractive geometric properties several of which are dictated by properties of the…

We lay down the foundations for a systematic study of differentiable and algebraic supervarieties, with a special attention to supergroups.

We survey what is known about various special types of submanifolds of contact manifolds and discuss their role in the development of contact geometry.

Assuming that every hyperbolic group is residually finite, we prove the congruence subgroup property for mapping class groups of hyperbolic surfaces of finite type. Under the same assumption, it follows that profinitely equivalent…