Related papers: Surface Groups In The Group Of Germs Of Analyticdi…
We consider the space of embeddings of finitely many circles that bound disks in non-positively curved surfaces. We index the connected components of this space with finite rooted trees and show that the connected components are classifying…
We show that certain classes of graphs of free groups contain surface subgroups, including groups with positive $b_2$ obtained by doubling free groups along collections of subgroups, and groups obtained by "random" ascending HNN extensions…
We give a classification of generic coadjoint orbits for the groups of symplectomorphisms and Hamiltonian diffeomorphisms of a closed symplectic surface. We also classify simple Morse functions on symplectic surfaces with respect to actions…
This article is a revised version of the talk I gave at the conference ``Beauville Surfaces and groups'' held in Newcastle in June 2012. It presents some group theoretical methods to give bounds on the number of connected components of the…
T. Mostowski showed that every (real or complex) germ of an analytic set is homeomorphic to the germ of an algebraic set. In this paper we show that every (real or complex) analytic function germ, defined on a possibly singular analytic…
Complete sets of bases of differential invariants, operators of invariant differentiation and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of…
We determine which amalgamated products of surface groups identified over multiples of simple closed curves are not fundamental groups of 3-manifolds. We prove each surface amalgam considered is virtually the fundamental group of a…
A skew-morphism $\varphi$ of a finite group $A$ is a permutation on $A$ such that $\varphi(1)=1$ and $\varphi(xy)=\varphi(x)\varphi^{\pi(x)}(y)$ for all $x,y\in A$ where $\pi:A\to\mathbb{Z}_{|\varphi|}$ is an integer function. A…
The Surface Group Conjectures are statements about recognising surface groups among one-relator groups, using either the structure of their finite-index subgroups, or all subgroups. We resolve these conjectures in the two generator case.…
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.
In this paper, we briefly review some of the known results concerning the cohomological structures of the mapping class group of surfaces, the outer automorphism group of free groups, the diffeomorphism group of surfaces as well as various…
We are concerned with orderable groups and particularly those with orderings invariant not only under multiplication, but also under a given automorphism or family of automorphisms. Several applications to topology are given: we prove that…
We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification of such embeddings in a wide range.
The main result of this paper is a Pfaffian formula for the partition function of the dimer model on a graph G embedded in a closed, possibly non-orientable surface S. This formula is suitable for computational purposes, and it is obtained…
We construct an infinite dimensional real analytic manifold structure for the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is real analytic if it extends to a holomorphic map on some…
In this paper we examinate some phenomena arising when a holomorphic germ is analytically continued.
We present a way of constructing and deforming diffeomorphisms of manifolds endowed with a Lie group action. This is applied to the study of exotic diffeomorphisms and involutions of spheres and to the equivariant homotopy of Lie groups.
We provide a data structure for maintaining an embedding of a graph on a surface (represented combinatorially by a permutation of edges around each vertex) and computing generators of the fundamental group of the surface, in amortized time…
Following the recent advances in the study of groups of circle diffeomorphisms, we describe an efficient way of classifying the topological dynamics of locally discrete, finitely generated, virtually free subgroups of the group…
We describe the effect of rational singularities on the Brauer group of a surface, and compute the Brauer groups of all singular del Pezzo surfaces over an algebraically closed field.