Related papers: Fixed Points of abelian actions

We characterize finite sets $S$ of nonwandering points for generic diffeomorphisms $f$ as those which are {\em uniformly bounded}, i.e., there is an uniform bound for small perturbations of the derivative of $f$ along the points in $S$ up…

In this paper, we give a characterization for any abelian subgroup G of a lie group of diffeomorphisms maps of C^n, having a somewhere dense orbit G(x), x in C^n: G(x) is somewhere dense in C^n if and only if there are f_{1},....,f_{2n+1 in…

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…

Let $BS(1,n) =< a, b \ | \ aba^{-1} = b^n >$ be the solvable Baumslag-Solitar group, where $ n\geq 2$. It is known that BS(1,n) is isomorphic to the group generated by the two affine maps of the real line: $f_0(x) = x + 1$ and $h_0(x) = nx…

We prove that the group of diffeomorphisms of the interval $[0,1]$ contains surface groups whose action on $(0,1)$ has no global fix point, is topologically transitive, and such that only countably many points of the interval $(0,1)$ have…

In this article, we derive a common fixed point result for a pair of single valued and set-valued mappings on a metric space having graphical structure. In this case, the set-valued map is assumed to be closed valued instead of closed and…

In this paper, we prove that each automorphism of the Torelli group of a surface is induced by a diffeomorphism of the surface, provided that the surface is a closed, connected, orientable surface of genus at least 3. This result was…

Let $q$ be a prime and $A$ an elementary abelian group of order at least $q^3$ acting by automorphisms on a finite $q'$-group $G$. It is proved that if $|\gamma_{\infty}(C_{G}(a))|\leq m$ for any $a\in A^{\#}$, then the order of…

We prove a criterion for an isometric action of a Lie group on a Riemannian manifold to be polar. From this criterion, it follows that an action with a fixed point is polar if and only if the slice representation at the fixed point is polar…

In this paper we study certain analogues of the map defined by Alain Connes, which follows an idea of Atiyah in trying to simplify the proof of Feit-Thompson theorem. It turns out that the the non-zero fixed points of the map can be…

We prove that every distortion element in the group of diffeomorphisms of the 2-sphere which has some recurrent point that is not fixed is an irrational pseudo-rotation. Moreover we prove that the differential of a distortion element in the…

We study the homotopy fixed points under the Frobenius endomorphism on the stable $\mathbb A^1$-homotopy category of schemes in characteristic $p>0$ and prove a rigidity result for cellular objects in these categories after inverting $p$.…

We give a short, mostly elementary and self-contained proof of the classical result that the groups of diffeomorphisms, homeomorphisms, and homotopy equivalences of a surface have the same group of connected components.

Let $S$ be a right reversible semitopological semigroup, and let $\operatorname{LUC}(S)$ be the space of left uniformly continuous functions on $S$. Suppose that $\operatorname{LUC}(S)$ has a left invariant mean. Let $K$ be a weakly compact…

We prove that if a continuous piecewise-smooth map on $\mathbb{R}^n$ is comprised of two linear functions, has a bounded orbit, and satisfies a certain non-degeneracy condition, then it has a fixed point. The result has important…

The special linear group G=SL_n(Z[x1,...,xk]) (n at least 3 and k finite) is called the universal lattice. Let n be at least 4, p be any real number in (1,\infty). The main result is the following: any finite index subgroup of G has the…

We show that for the standard map family, for all values of the parameter, except one, the mapping has positive topological entropy. The main tool is the following result. Let $S$ be a compact connected orientable surface and $f:S…

We show that any action of a finite group on a finitely presentable group arises as the action of the group of self-homotopy equivalences of a space on its fundamental group. In doing so, we prove that any finite connected (abstract)…

The result of Boyce and Huneke gives rise to a 1-dimensional continuum, which is the intersection of a descending family of disks, that admits two commuting homeomorphisms without a common fixed point.

In this note, we deal with the fixed points of an endofunctor $F: \mathcal{C} \longrightarrow \mathcal{C}$. Three classes of fixed points are introduced, and the case when $F$ is an endomorphism of a category with pretopology is…