Related papers: Small index subgroups of the mapping class group

We study the topological index of some irregular surfaces that we call generalized Lagrangian. We show that under certain hypotheses on the base locus of the Lagrangian system the topological index is non-negative. For the minimal surfaces…

We show that any simple group of Morley rank 4 must be a bad group with no proper definable subgroups of rank larger than 1. We also give an application to groups acting on sets of Morley rank 2.

This note serves to record examples of diffeomorphisms of closed smooth $4$-manifolds $X$ that are homotopic but not pseudoisotopic to the identity, and to explain why there are no such examples when $X$ is orientable and its fundamental…

This paper has 3 principal goals: (1) to survey what is know about mapping class and Torelli groups of simply connected compact Kaehler manifolds, (2) supplement these results, and (3) present a list of questions and open problems to…

In this article, we show that the critical catenoid, as a free boundary minimal surface of the unit ball in $\mathbb{R}^3$, has index $4$. We also prove that a free boundary minimal surface of the unit ball in $\mathbb{R}^3$, that is not a…

We prove that the separating curve graph of a connected, compact, orientable surface with genus at least 3 and a single boundary component is not relatively hyperbolic. This completes the classification of when the separating curve graph is…

We construct a minimal generating set of the level 2 mapping class group of a nonorientable surface of genus $g$, and determine its abelianization for $g\ge4$.

given two minimal surfaces embedded in $\S3$ of genus $g$ we prove the existence of a sequence of non-congruent compact minimal surfaces embedded in $\S3$ of genus $g$ that converges in $C^{2,\alpha}$ to a compact embedded minimal surface…

We notice that the class of nontrivial groups without proper subgroups of finite index is not elementary, because some groups in this class, such as $\mathbb Q*\mathbb Q$, have ultrapowers that map homomorphically onto $\mathbb Z/p\mathbb…

In this note we prove that there is no constant $C$, depending on the genus of the surface, such that every element in the mapping class group can be written as a product of at most $C$ torsion elements, answering a question of T. E.…

In this note we show that many subgroups of mapping class groups of infinite-type surfaces without boundary have trivial centers, including all normal subgroups. Using similar techniques, we show that every nontrivial normal subgroup of a…

In this paper, we prove that any closed orientable 3-manifold $M$ other than $\#^k S^1\times S^2$ and $S^3$ satisfies the following properties: (1) For any compact orientable 4-manifold $N$ bounded by $M$, the inclusion does not induce an…

We employ partitioning methods, in the spirit of Montiel--Ros but here recast for general actions of compact Lie groups, to prove effective lower bounds on the Morse index of certain families of closed minimal hypersurfaces in the round…

For any infinite-type surface $S$, a natural question is whether the homology of its mapping class group contains any non-trivial classes that are supported on (i) a compact subsurface or (ii) a finite-type subsurface. Our purpose here is…

We study here the tautological rings of the moduli spaces of compact Riemann surfaces of genus 1,2,3 and 4 with marked points. The paper presents the complete descriptions of these rings by describing the groups of all degrees.

We construct a geometric model for the mapping class group M of a non-exceptional oriented surface of finite type and use it to show that the action of M on the compact Hausdorff space of complete geodesic laminations is topologically…

We show that every countable subgroup $G<\rm GL_+(2,\mathbb{R})$ without contracting elements is the Veech group of a tame translation surface $S$ of infinite genus, for infinitely many different topological types of $S$. Moreover, we prove…

We give an alternate proof of the left-orderability of the mapping class group of a connected oriented infinite-type surface with a non-empty boundary. Our main strategy involves the inductive construction of a countable stable Alexander…

We prove that for each sufficiently complicated orientable surface $S$, there exists an infinite image linear representation $\rho$ of $\pi_1(S)$ such that if $\gamma\in\pi_1(S)$ is freely homotopic to a simple closed curve on $S$, then…

We show that there are infinitely many Nielsen equivalence classes of the mapping class group of a closed oriented surface of genus at least eight.