Related papers: A free action of a finite group on 3-sphere equiva…
The orbit spaces of free S^0-actions on the mod 2 cohomology product of three spheres, S^n x S^m x S^l, 1 <= n <= m <= l have been determined in [6]. In this paper, we extend these findings to free S^1-actions on the rational cohomology…
We give a simplified proof of J. A. Wolf's classification of finite groups that can act freely and isometrically on a round sphere of some dimension. We slightly improve the classification by removing some non-obvious redundancy. The groups…
We study finite group actions on smooth manifolds of the form $M\#\Sigma$, where $\Sigma$ is an exotic $n$-sphere and $M$ is a closed aspherical space form. We give a classification result for free actions of finite groups on $M\#\Sigma$…
This is a survey on upper and lower bounds for finite group actions on bounded surfaces, 3-dimensional handlebodies and closed handles, handlebodies in arbitrary dimensions and finite graphs (the common feature of these objects is that all…
We classify contact toric 3-manifolds up to contactomorphism, through explicit descriptions, building off of work by Lerman [Lerman03]. As an application, we classify all contact structures on 3-manifolds that can be realised as a concave…
A group action H on X is called "telescopic" if for any finitely presented group G, there exists a subgroup H' in H such that G is isomorphic to the fundamental group of X/H'. We construct examples of telescopic actions on some CAT[-1]…
Given a complex manifold endowed with a $\mathbb{C}^\times$-action and a DQ-algebra equipped with a compatible holomorphic Frobenius action (F-action), we prove that if the $\mathbb{C}^\times$-action is free and proper, then the category of…
We express the total space of a principal circle bundle over a connected sum of two manifolds in terms of the total spaces of circle bundles over each summand, provided certain conditions hold. We then apply this result to provide…
We show that a free period three action on the three-sphere is standard, i.e. the quotient is homeomorphic to a lens space. We use a minimax argument involving sweepouts.
We prove that if a finite group $G$ has a representation with fixity $f$, then it acts freely and homologically trivially on a finite CW-complex homotopy equivalent to a product of $f+1$ spheres. This shows, in particular, that every finite…
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…
The standard actions of finite groups on spheres S^d are linear actions, i.e. by finite subgroups of the orthogonal group O(d+1). We prove that, in each dimension d>5, there is a finite group G which admits a faithful, topological action on…
In this paper we introduce the notion of orbit equivalence for semigroup actions and the concept of generalized linear control system on smooth manifold. The main goal is to prove that, under certain conditions, the semigroup system of a…
This paper gives the cohomology classification of finitistic spaces X equipped with free actions of the group G = S3 and the orbit space X/G is the integral or mod 2 cohomology quaternion projective space HPn. We have proved that X is the…
This paper establishes a Borsuk-Ulam type theorem for PL-manifolds with a finite group action, depending on the free equivariant cobordism class of a manifold. In particular, necessary and sufficient conditions are considered for a manifold…
A discrete group G has periodic cohomology over R if there is an element in a cohomology group, cup product with which induces an isomorphism in cohomology after a certain dimension. Adem and Smith showed if R = Z, then this condition is…
In this paper we first survey some basic results in the cohomology of finite groups, and then discuss recent work on constructing free actions of finite groups on products of spheres.
We give necessary and sufficient conditions under which a quasi-action of any group on an arbitrary metric space can be reduced to a cobounded isometric action on some bounded valence tree, following a result of Mosher, Sageev and Whyte.…
Let $X$ be a Fano threefold and $\C ^* \times X\rightarrow X$ an algebraic action. Then $X$ has a $S^1$-invariant K\"ahler structure and the corresponding $S^1$-action admits an equivariant moment map which is at the same time a perfect…
In this paper we use free iterated actions and the iterated discrete degree of symmetry to obtain rigidity results on aspherical manifolds. We also introduce the concept of the length of an iterated action and we study it for nilmanifolds,…