相关论文: On the group action of $Mod(M,F)$ on the disk comp…

Let (V,W;F) be a weakly reducible, unstabilized, genus three Heegaard splitting in an orientable, irreducible 3-manifold M. In this article, we prove that either the disk complex D(F) is contractible or F is critical. Hence, the topological…

We consider finite group-actions on closed, orientable and nonorientable 3-manifolds; such a finite group-action leaves invariant the two handlebodies of a Heegaard splitting of M of some genus g. The maximal possible order of a finite…

Let $M$ be an orientable, irreducible $3$-manifold and $(\mathcal{V},\mathcal{W};F)$ a weakly reducible, unstabilized Heegaard splitting of $M$ of genus at least three. In this article, we define an equivalent relation $\sim$ on the set of…

Let (V,W;F) be a weakly reducible, unstabilized, genus three Heegaard splitting in an orientable, irreducible 3-manifold M and DVW(F) the subset of the disk complex D(F) consisting of simplices having at least one vertex from V and at least…

We consider finite group-actions on closed, orientable and nonorientable 3-manifolds M which preserve the two handlebodies of a Heegaard splitting of M of some genus g > 1 (maybe interchanging the two handlebodies). The maximal possible…

Let $M$ be a closed orientable 3-manifold with a genus two Heegaard splitting $(V_1, V_2; F)$ and a non-trivial JSJ-decomposition, where all components of the intersection of the JSJ-tori and $V_i$ are not $\partial$-parallel in $V_i$ for…

Let G be a finitely generated group having the property that any action of any finite-index subgroup of G by homeomorphisms of the circle must have a finite orbit. (By a theorem of E.Ghys, lattices in simple Lie groups of real rank at least…

Let $M$ be a closed orientable 3-manifold with a genus two Heegaard splitting $(V_1, V_2; F)$ and a non-trivial JSJ-decomposition, where all components of the intersection of the JSJ-tori and $V_i$ are not $\partial$-parallel in $V_i$ for…

Let $f:M\to \mathbb{R}$ be a Morse function on a smooth closed surface, $V$ be a connected component of some critical level of $f$, and $\mathcal{E}_V$ be its atom. Let also $\mathcal{S}(f)$ be a stabilizer of the function $f$ under the…

We discuss properties of orbits of (semi)group actions on locally compact groups G. In particular, we show that if a compactly generated locally compact abelian group acts distally on G then the closure of each of its orbits is a minimal…

In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of…

We consider orientation-preserving actions of a finite group G on the 3-sphere S^3 (and also on Euclidean space R^3). By the geometrization of finite group actions on 3-manifolds, if such an action is smooth then it is conjugate to an…

Let $G$ be a group. The orbits of the natural action of $Aut(G)$ on $G$ are called "automorphism orbits" of $G$, and the number of automorphism orbits of $G$ is denoted by $\omega(G)$. In this paper we prove that if $G$ is an FC-group with…

We study the topology of compact manifolds with a Lie group action for which there are only finitely many non-principal orbits, and describe the possible orbit spaces which can occur. If some non-principal orbit is singular, we show that…

We enumerate Hurwitz orbits of shortest reflection factorizations of an arbitrary element in the infinite family $G(m, p, n)$ of complex reflection groups. As a consequence, we characterize the elements for which the action is transitive…

Let $M$ be an orientable, irreducible $3$-manifold admitting a weakly reducible genus three Heegaard splitting as a minimal genus Heegaard splitting. In this article, we prove that if $[f]$, $[g]\in Mod(M)$ give the same correspondence…

We give a length one projective resolution of the trivial module for the groupoid of a semi-saturated partial action (in the sense of Exel) of a free group on a compact Hausdorff and totally disconnected space. As a consequence we obtain an…

This paper is about topological rigidity of diagonal group actions on the homogeneous $\SL_4\big(\F(\!(t^{-1})\!)\big)/\SL_4(\F[t])$ where $\F$ is a finite field of characteristic $3$. We show that there is a non-closed relatively compact…

An action of a finite group $G$ is a pair $(S,\hat{G})$, where $S$ is a compact Riemann surface of genus $g \geqslant 2$ and $\hat{G} \leqslant {\rm Aut}(S)$ is isomorphic to $G$. To each action $(S,\hat{G})$ there is associated a signature…

Let G be the Heisenberg group of real lower triangular 3x3 matrices with unit diagonal. A locally free smooth action of G on a manifold M^4 is given by linearly independent vector fields X_1, X_2, X_3 such that X_3 = [X_1,X_2] and [X_1,X_3]…