Related papers: Mapping class group and global Torelli theorem for…
The group of extensions (as in the title), endowed with something like a connection at Archimedean infinity, is isomorphic to the ad\'ele-class group of $\Q$: which is a topological group with interesting Haar measure.}
In this paper we prove an inverse function theorem in derived differential geometry. More concretely, we show that a morphism of curved $L_\infty$ spaces which is a quasi-isomorphism at a point has a local homotopy inverse. This theorem…
We carefully present an elementary proof of the well known theorem that each homotopy group (or, in degree zero, pointed set) of the inverse limit of a tower of fibrations maps naturally onto the inverse limit of the homotopy groups (or, in…
We find all possible isomorphisms and 3-birational maps (i.e., birational maps which induce an isomorphism between open subsets whose respective complements have codimension at least 3) between moduli spaces of parabolic vector bundles with…
This self-contained paper is part of a series \cite{FF2,FF3} on actions by diffeomorphisms of infinite groups on compact manifolds. The two main results presented here are: 1) Any homomorphism of (almost any) mapping class group or…
The aim of this paper is to introduce a group containing the mapping class groups of all genus zero surfaces. Roughly speaking, such a group is intended to be a discrete analogue of the diffeomorphism group of the circle. One defines indeed…
If E is a non-isotrivial elliptic curve over a global function field F of odd characteristic we show that certain Mordell-Weil groups of E have 1-dimensional eigenspace relative to a fixed complex ring class character provided that the…
The aim of this paper is to survey some known results about mapping class group quotients by powers of Dehn twists, related to their finite dimensional representations and to state some open questions. One can construct finite quotients of…
We show that mapping class groups of surfaces of genus at least two contain elements of infinite order that are not conjugate to their inverses, but whose powers have bounded torsion lengths. In particular every homogeneous…
We consider a homological enlargement of the mapping class group, defined by homology cylinders over a closed oriented surface (up to homology cobordism). These are important model objects in the recent Goussarov-Habiro theory of…
For a homeomorphism $T \colon X \to X$ of a Cantor set $X$, the mapping class group $\mathcal{M}(T)$ is the group of isotopy classes of orientation-preserving self-homeomorphisms of the suspension $\Sigma_{T}X$. The group $\mathcal{M}(T)$…
In the Cayley graph of the mapping class group of a closed surface, with respect to any generating set, we look at a ball of large radius centered on the identity vertex, and at the proportion among the vertices in this ball representing…
A crosscap transposition is an element of the mapping class group of a nonorientable surface represented by a homeomorphism supported on a one-holed Klein bottle and swapping two crosscaps. We prove that the mapping class group of a compact…
This is the second of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we develop a basic machinery for studying homotopy classes of such maps. It contains two parts: (1) the…
In this note, I study a comparison map between a motivic and \'{e}tale cohomology group of an elliptic curve over $\mathbb{Q}$ just outside the range of Voevodsky's isomorphism theorem. I show that the property of an appropriate version of…
We prove that every topological conjugation between two germs of singular holomorphic curves in the complex plane is homotopic to another conjugation which extends homeomorphically to the exceptional divisors of their minimal…
The mapping class group of an orientable surface, which records its symmetries up to isotopy, plays a central role in low-dimensional topology. This chapter explores the foundational problem of determining minimal generating sets for these…
We show that continuous epimorphisms between a class of subgroups of mapping class groups of orientable infinite-genus 2-manifolds with no planar ends are always induced by homeomorphisms. This class of subgroups includes the pure mapping…
For almost finite groupoids, we study how their homology groups reflect dynamical properties of their topological full groups. It is shown that two clopen subsets of the unit space has the same class in H_0 if and only if there exists an…
Let $S_g$ be a closed, oriented surface of genus $g$, and let $\operatorname{Mod}(S_g)$ denote its mapping class group. The Torelli group $\mathcal{I}_g$ is the subgroup of $\operatorname{Mod}(S_g)$ consisting of mapping classes that act…