Related papers: Mapping class groups for 2-orbifolds
The spaces of triangulations of a given manifold have been widely studied. The celebrated theorem of Pachner~\cite{Pachner} says that any two triangulations of a given manifold can be connected by a sequence of bistellar moves, or Pachner…
We present examples of prequantizations over integral symplectic manifolds which admit infinitely many smoothly trivial contact mapping classes. These classes are given by the connected components of the strict contactomorphism group which…
In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between…
We introduce and study asymptotically rigid mapping class groups of certain infinite graphs. We determine their finiteness properties and show that these depend on the number of ends of the underlying graph. In a special case where the…
In this paper we compute the mapping class group of simply-connected closed smooth manifolds $M$ with integral homology $H_{*}(M) \cong \mathbb Z \oplus \mathbb Z \oplus \mathbb Z$ provided that $\dim M \ne 4$.
We study the Picard groups of moduli spaces of smooth complex projective curves that have a group of automorphisms with a prescribed topological action. One of our main tools is the theory of symmetric mapping class groups. In the first…
: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…
In this article, we introduce a new family of groups, called Chambord groups and constructed from braided strand diagrams associated to specific semigroup presentations. It includes the asymptotically rigid mapping class groups previously…
A class of groups is investigated, each of which has a fairly simple presentation . For example the group $R = (a, b, c, d | a^3 = b^3 = c^3 = d^3 = 1, ba^{-1} =dc^{-1}, ca^{-1} = db^{-1}) $ is in the class. Such a group does not have as a…
We are concerned with mapping class groups of surfaces with nonempty boundary. We present a very natural method, due to Thurston, of finding many different left orderings of such groups. The construction involves equipping the surface with…
The mapping class group of a non-exceptional oriented surface of finite type admits a biautomatic structure.
We investigate the separability of several well known classes of subgroups of the mapping class group of a surface.
Complex braid groups are the natural generalizations of braid groups associated to arbitrary (finite) complex reflection groups. We investigate several methods for computing the homology of these groups. In particular, we get the Poincar\'e…
This paper presents fifteen problems about mapping class groups. It is an expanded and updated version of the author's preprint "Ten problems on the mapping class groups". The paper will appear in the book "Problems on Mapping Class Groups…
We survey the analogy between Kleinian groups and subgroups of the mapping class group of a surface.
This paper is a survey of the relationship between labelled configuration spaces, mapping class groups with marked points and function spaces. In particular, we collect calculations of the cohomology groups for the mapping class groups of…
We define formal orbifolds over an algebraically closed field of arbitrary characteristic as curves together with some branch data. Their \'etale coverings and their fundamental groups are also defined. These fundamental group approximates…
A Riemannian orbifold is a mildly singular generalization of a Riemannian manifold that is locally modeled on $R^n$ modulo the action of a finite group. Orbifolds have proven interesting in a variety of settings. Spectral geometers have…
The present paper are the notes of a mini-course addressed mainly to non-experts. It purpose it to provide a first approach to the theory of mapping class groups of non-orientable surfaces.
We describe a cocompact model for the classifying space for proper actions of the mapping class group of a surface with punctures and boundary components. Our construction relies on a known model for the case of a closed surface and uses an…