Related papers: Surface Groups In The Group Of Germs Of Analyticdi…

We study surface links whose link groups are free abelian, and construct various stimulating and highly non-trivial examples of such surface links.

Let $M$ be the circle or a compact interval, and let $\alpha=k+\tau\ge1$ be a real number such that $k=\lfloor \alpha\rfloor$. We write $\mathrm{Diff}_+^{\alpha}(M)$ for the group of $C^k$ diffeomorphisms of $M$ whose $k^{th}$ derivatives…

We study groups of homeomorphisms of R, each of whose elements have at most one fixed point. In particular we prove that any such group of C^2 diffeomorphisms is topologically conjugate to an affine group.

We construct the equivariant analytic lattice cohomology associated with the analytic type of a complex normal surface singularity whenever the link is a rational homology sphere. It is the categorification of the equivariant geometric…

We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.

In \cite{K-rig}, a map $\beta:\mathcal R\to\mathcal{B}el$ from the set $\mathcal R$ of equivalence classes of rigid germs of finite morphisms branched in germs of curves having $ADE$ singularity types onto the set $\mathcal{B}el$ of…

We develop technics of birational geometry to study automorphisms of affine surfaces admitting many distinct rational fibrations, with a particular focus on the interactions between automorphisms and these fibrations. In particular, we…

The generators of the group of birational automorphisms of any Severi-Brauer surface non-isomorphic over an algebraically non-closed field to the projective plane are explicitly described.

We obtain a minimal generating set of involutions for the level 2 subgroup of the mapping class group of a closed nonorientable surface.

We prove that the action of the semigroup generated by a $C^r$ generic pair of area-preserving diffeomorphisms of a compact orientable surface is transitive.

In this paper we study random representations of fundamental groups of surfaces into special unitary groups. The random model we use is based on a symplectic form on moduli space due to Atiyah, Bott, and Goldman. Let $\Sigma_{g}$ denote a…

We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.

We study orbit closures and stationary measures for groups of automorphisms of $p$-adic affine surfaces.

We study collections of curves in generic position on a closed surface whose complement consists of one disk only, up to orientation-preserving homeomorphism of the surface. We define a surgery operation on the set of such collections and…

We prove that any complex or real analytic set or function germ is topologically equivalent to a germ defined by polynomial equations whose coefficients are algebraic numbers.

A surface in the 4-sphere is trivially embedded, if it bounds a 3-dimensional handle body in the 4-sphere. For a surface trivially embedded in the 4-sphere, a diffeomorphism over this surface is extensible if and only if this preserves the…

We study the structure of abelian subgroups of Galois groups of function fields of surfaces.

The topic of the paper is the study of germs of local holomorphisms $f$ between $C^n$ and $C^{n'}$ such that $f(M)\subset M'$ and $df(T^cM)=T^cM'$ for $M\subset C^n$ and $M'\subset C^{n'}$ generic real-analytic CR submanifolds of arbitrary…

We give a geometric description of a certain class of epimorphisms between complex reflection groups. We classify these epimorphisms, which can be interpreted as ``morphisms'' between the diagrams symbolizing standard presentations by…

We associate to any irreducible germ S of complex quasi-ordinary hypersurface an analytically invariant semigroup. We deduce a direct proof (without passing through their embedded topological invariance) of the analytical invariance of the…