Related papers: Fixed Points of abelian actions on $S^2$

We show that if $G$ is a countable amenable group acting on a uniquely arcwise connected continuum $X$, then $G$ has either a fixed point or a 2-periodic point in $X$.

We develop the basic theory of Maurer-Cartan simplicial sets associated to (shifted complete) $L_\infty$ algebras equipped with the action of a finite group. Our main result asserts that the inclusion of the fixed points of this equivariant…

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 extend to binary relational systems the notion of compact and normal structure, introduced by J.P.Penot for metric spaces, and we prove that for the involutive and reflexive ones, every commuting family of relational homomorphisms has a…

Let $G$ be connected nilpotent Lie group acting locally on a real surface $M$. Let $\varphi$ be the local flow on $M$ induced by a $1$-parameter subgroup. Assume $K$ is a compact set of fixed points of $\varphi$ and $U$ is a neighborhood of…

In this paper, we discuss characterizations of common fixed points of commutative semigroups of nonexpansive mappings. We next prove convergence theorems to a common fixed point. We finally discuss nonexpansive retractions onto the set of…

Let $H$ be a group acting on a simply-connected diagrammatically reducible combinatorial 2-complex $X$ with fine 1-skeleton. If the fixed point set $X^ H$ is non-empty, then it is contractible. Having fine 1-skeleton is a weaker version of…

We show that, for each finite algebra A, either it has symmetric term operations of all arities or else some finite algebra in the variety generated by A has two automorphisms without a common fixed point. We also show this two-automorphism…

We prove that a finitely generated group contains a sequence of non-trivial elements which converge to the identity in every compact homomorphic image if and only if the group is not virtually abelian.

The main purpose of this work is to extend the properties of multivalued transformations to the integral type transformations and to obtain the existence of fixed points under F-contraction. In addition, the results of this study were…

We show that if $X$ is a complete metric space with uniform relative normal structure and $G$ is a subgroup of the isometry group of $X$ with bounded orbits, then there is a point in $X$ fixed by every isometry in $G$. As a corollary, we…

We show that any group $G$ is contained in some sharply 2-transitive group $\mathcal{G}$ without a non-trivial abelian normal subgroup. This answers a long-standing open question. The involutions in the groups $\mathcal{G}$ that we…

Plante-Thurston proved that every nilpotent subgroup of $\Diff^2(S^1)$ is abelian. One of our main results is a sharp converse: $\Diff^1(S^1)$ contains every finitely-generated, torsion-free nilpotent group.

In this paper, we discuss the existence of fixed points for integral type contractions in uniform spaces endowed with both a graph and an $E$-distance. We also give two sufficient conditions under which the fixed point is unique. Our main…

We extend the construction of generalized fixed point algebras to the setting of locally compact quantum groups - in the sense of Kustermans and Vaes - following the treatment of Marc Rieffel, Ruy Exel and Ralf Meyer in the group case. We…

Based on the recently developed theory of random sequential compactness, we prove the random Kakutani fixed point theorem in random normed modules: if G is a random sequentially compact L0-convex subset of a random normed module, then every…

Given a saturated fusion system $\mathcal{F}$ over a $2$-group $S$, we prove that $S$ is abelian provided any element of $S$ is $\mathcal{F}$-conjugate to an element of $Z(S)$. This generalizes a Theorem of Camina--Herzog, leading to a…

Let B be any Lp space for p in (1,infty) or any Banach space isomorphic to a Hilbert space, and k be a nonnegative integer. We show that if n is at least 4, then the universal lattice Gamma =SL_n (Z[x1,...,xk]) has property (F_B) in the…

In this paper we are going to prove a very general fixed point theorem for mappings acting in partial metric spaces. In that theorem we impose some conditions on behavior of considered mappings on orbits and a condition relating orbits of…

We show that the actions and indexes of fixed points of a Hamiltonian diffeomorphism with finitely many periodic points must satisfy certain relations, provided that the quantum cohomology of the ambient manifold meets an algebraic…