Related papers: Equivariant Mapping Class Group and Orbit Braid Gr…

We consider Thompson's groups from the perspective of mapping class groups of surfaces of infinite type. This point of view leads us to the braided Thompson groups, which are extensions of Thompson's groups by infinite (spherical) braid…

Let $X$ be a smooth scheme with an action of a reductive algebraic group $G$ over an algebraically closed field $k$ of characteristic zero. We construct an action of the extended affine Braid group on the $G$-equivariant absolute derived…

We establish a connection between two well-studied spaces of countable groups: the space of group operations and the space of marked groups. This connection shows that the two spaces are equivalent in terms of generic properties in the…

In this paper we construct a homomorphism of the affine braid group $Br_n^{aff}$ in the convolution algebra of the equivariant matrix factorizations on the space $\overline{\mathcal{X}}_2=\mathfrak{b}_n\times GL_n\times\mathfrak{n}_n$…

We compute equivariant fundamental classes of orbits in GL(2)-representations. As applications, we find degrees of the orbit closures corresponding to elliptic fibrations and self-maps of the projective line.

Given a smooth action of the sphere $\mathbb S^3$ on a manifold $M$, we have previously constructed a Gysin sequence relating the cohomology of the manifold $M$ and that of the orbit space $M/\mathbb S^3$. This sequence involves an exotic…

We study a geometric action on a CAT(0) space of a finite index subgroup of the quotient group of the braid group on 4 strands by its center.

We show that the {\it full} mapping class group of any orientable closed surface with punctures admits a cocompact classifying space for proper actions of dimension equal to its virtual cohomological dimension. This was proved for closed…

We prove that the quantum toroidal algebras $\mathcal{E}_\mathbf{s}$ associated with different root systems $\mathbf{s}$ of $\mathfrak{gl}_{m|n}$ type are isomorphic. We also show the existence of Miki automorphism of…

Let G be a connected reductive group. In this paper we are studying the invariant theory of symplectic G-modules. Our main result is that the invariant moment map is equidimensional. We deduce that the categorical quotient is a fibration…

We deduce that the fundamental groups of the orbit configuration spaces of an effective and properly discontinuous action of a discrete group on a connected aspherical 2-manifold, with isolated fixed points, fit into a four-term exact…

Given a smooth partial action $\alpha$ of a Lie groupoid $G$ on a smooth manifold $M,$ we provide necessary and sufficient conditions for $\alpha$ to be globalizable with smooth globalization. As an application, we provide results on the…

The closure of a braid in a closed orientable surface $\Sigma$ is a link in $\Sigma\times S^1$. We classify such closed surface braids up to isotopy and homeomorphism (with a small indeterminacy for isotopy of closed sphere braids),…

Equivariant indices have previously been defined in cases where either the group or the orbit space in question is compact. In this paper, we develop an equivariant index without assuming the group or the orbit space to be compact. This…

The group $G = GL_r(k) \times (k^\times)^n$ acts on $\mathbf{A}^{r \times n}$, the space of $r$-by-$n$ matrices: $GL_r(k)$ acts by row operations and $(k^\times)^n$ scales columns. A matrix orbit closure is the Zariski closure of a point…

We consider spaces of plane curves in the setting of algebraic geometry and of singularity theory. On one hand there are the complete linear systems, on the other we consider unfolding spaces of bivariate polynomials of Brieskorn-Pham type.…

For a given inverse semigroup action on a topological space, one can associate an \'etale groupoid. We prove that there exists a correspondence between the certain subsemigroups and the open wide subgroupoids in case that the action is…

We develop general techniques for computing the fundamental group of the configuration space of $n$ identical particles, possessing a generic internal structure, moving on a manifold $M$. This group generalizes the $n$-string braid group of…

We prove that there exists a geometric bijection between the sets of adjoint and coadjoint orbits of a semidirect product, provided a similar bijection holds for particular subgroups. We also show that under certain conditions the homotopy…

In the study of the relation between the mapping class group M of a surface and the theory of finite-type invariants of homology 3-spheres, three subgroups of the mapping class group play a large role. They are the Torelli group, the…