Related papers: Topological characterization of torus groups
We characterize all groups which can occur as the topological symmetry group or the orientation preserving topological symmetry group of some embedding of the Petersen graph in S^3.
In order to make the fundamental group, one of the most well known invariants in algebraic topology, more useful and powerful some researchers have introduced and studied various topologies on the fundamental group from the beginning of the…
In this paper we complete the classification of topological symmetry groups for complete graphs $K_n$ by characterizing which $K_n$ can have a cyclic group, a dihedral group, or a subgroup of $D_m \times D_m$ where $m$ is odd, as its…
Topological groupoids admit various types of morphisms. We push these notions to the level of continuous groupoid actions to obtain various types of groupoid action morphisms. Some dynamical properties and their relation to these morphisms…
A toric manifold is a compact non-singular toric variety equipped with a natural half-dimensional compact torus action. A torus manifold is an oriented, closed, smooth manifold of dimension $2n$ with an effective action of a compact torus…
We describe an algorithm that constructs a list of all topological types of holomorphic actions of a finite group on a compact Riemann surface $C$ of genus at least $g \geq 2$ with $C/G \cong \mathbb{P}^1$.
We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.
This is a survey of topological properties of open, complete nonpositively curved manifolds which may have infinite volume. Topics include topology of ends, restrictions on the fundamental group, as well as a review of known examples.
A toric arrangement is a finite collection of codimension-$1$ subtori in a torus. These subtori stratify the ambient torus into faces of various dimensions. Let $f_i$ denote the number of $i$-dimensional faces; these so-called face numbers…
We consider a class of groups, called groups of F-type, which includes some known and important classes like Fuchsian groups of geometric rank $\ge 3$, surface groups of genus $\ge 2$, cyclically pinched one-relator groups and torus-knot…
This is a paper in Analytic Topology.
On objects of a triangulated category with a stability condition, we construct a topology.
We present a simple-to-apply criterion for recognizing topological groups that are (locally) homeomorphic to LF-spaces.
We give a formula for the character of the representation of the symmetric group $S_n$ on each isotypic component of the cohomology of the set of regular elements of a maximal torus of $SL_n$, with respect to the action of the centre.
This article establishes the variational principle of topological pressure for actions of sofic groupoids.
We give a simple topological construction of the Burau representations of the loop braid groups. There are four versions: defined either on the non-extended or extended loop braid groups, and in each case there is an unreduced and a reduced…
This is a survey on coarse geometry with an emphasis on coarse homology theories.
In this paper we describe orbits of automorphism group on a horospherical variety in terms of degrees of homogeneous with respect to natural grading locally nilpotent derivations. In case of (may be non-normal) toric varieties a description…
In this work we obtain sufficient conditions for a variety with a torus action of complexity one to have a finite number of automorphism group orbits.
New features of systems with non-trivial topology such as fractional quantum numbers, inequivalent quantizations, good operators, topological anomalies, etc. are described in the framework of an algebraic quantization procedure on a group.…