Related papers: Fixed points on null and tame flows for groups of …

We will prove the following theorems. The first theorem posits the existence of a fixed point for the actions of nilpotent Lie groups on nonpositively curved compact manifolds. The second theorem states that actions of solvable Lie groups…

We study fixed points of smooth torus actions on closed manifolds using fixed point formulas and equivariant elliptic genera. We also give applications to positively curved Riemannian manifolds with symmetry.

In this paper, we investigate the existence of fixed-point-free automorphisms for finite-dimensional Lie algebras. By a result of Jacobson, a Lie algebra admitting a fixed-point-free automorphism is solvable. We prove that such a Lie…

In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.

We study fixed point properties of the automorphism group of the universal Coxeter group Aut$(W_n)$. In particular, we prove that whenever Aut$(W_n)$ acts by isometries on complete $d$-dimensional CAT$(0)$ space with…

Smith theory says that the fixed point of a semi-free action of a group $G$ on a contractible space is ${\bb Z}_p$-acyclic for any prime factor $p$ of $G$. Jones proved the converse of Smith theory for the case $G$ is a cyclic group acting…

In this paper, we develop an Isabelle/HOL library of order-theoretic fixed-point theorems. We keep our formalization as general as possible: we reprove several well-known results about complete orders, often with only antisymmetry or…

The action of a finite group $G$ on a subshift of finite type $X$ is called free, if every point has trivial stabilizer, and it is called inert, if the induced action on the dimension group of $X$ is trivial. We show that any two free inert…

We prove that any finite subgroup $G \subset \Gamma_{{\boldsymbol{s}}}$ of the cluster modular group has fixed points in the cluster manifolds $\mathcal{A}_{\boldsymbol{s}}(\mathbb{R}_{>0})$ and…

We show that a continuous map or a continuous flow on $\R^{n}$ with a certain recurrence relation must have a fixed point. Specifically, if there is a compact set W with the property that the forward orbit of every point in $\R^{n}$…

We prove that if $F$ is a finitely generated abelian group of orientation preserving $C^1$ diffeomorphisms of $R^2$ which leaves invariant a compact set then there is a common fixed point for all elements of $F.$ We also show that if $F$ is…

We generalize the positive solution of the Frobenius conjecture and refinements thereof by studying the structure of groups that admit a fix-point-free automorphism satisfying an identity. We show, in particular, that for every polynomial…

We prove that a random group has fixed points when it isometrically acts on a CAT(0) cube complex. We do not assume that the action is simplicial.

We exhibit finitely generated torsion-free groups for which any action on any finite-dimensional CW-complex with finite Betti numbers has a global fixed point.

We study the automorphisms group action on a bounded domain in $\CC^n$ having a boundary point that is exponentially flat. Such a domain typically has a compact automorphism group. Our results enable us to generate many new examples.

We investigate fixed point properties for isometric actions of topological groups on a wide class of metric spaces, with a particular emphasis on Hilbert spaces. Instead of requiring the action to be continuous, we assume that it is…

We consider fully effective orientation-preserving smooth actions of a given finite group G on smooth, closed, oriented 3-manifolds M. We investigate the relations that necessarily hold between the numbers of fixed points of various…

In this paper, we examine Lie group actions on moduli spaces (sets themselves built as quotients by group actions) and their fixed points. We show that when the Lie group is compact and connected, we obtain a linear constraint. This…

Macbeath gave a formula for the number of fixed points for each non-identity element of a cyclic group of automorphisms of a compact Riemann surface in terms of the universal covering transformation group of the cyclic group. We observe…

Consider a closed coisotropic submanifold $N$ of a symplectic manifold $(M,\omega)$ and a Hamiltonian diffeomorphism $\phi$ on $M$. The main result of this article states that $\phi$ has at least the cup-length of $N$ many leafwise fixed…