2
votes
2answers
186 views

Action of Mapping Class Group on Arc complex

Suppose $S$ is a surface of finite type with nonempty boundary. Now consider the arc complex $\mathcal{A}$. The action of Mod(S)(mapping class group) on the set of all vertices has finitely many ...
8
votes
1answer
140 views

Counterexamples to analogue of Cannon conjecture in higher dimensions

It is known that a group $G$ acts geometrically on $\mathbb{H}^2$ if and only if $G$ is word-hyperbolic and its boundary $\partial G$ is homeomorphic to $S^1$. The analogous statement for ...
7
votes
1answer
382 views

Free $\mathbb{Z}_2$-actions match at some point

I have in front of me a proof of this lemma: If $f$ and $g$ are free $\mathbb{Z}_2$-actions on $S^1$, then $f(x)=g(x)$ for some $x \in S^1$. A $\mathbb{Z}_2$-action on the unit circle $S^1$ is a ...
1
vote
4answers
524 views

Variants of point fixed theorem

Let $E$ be a dual Banach space and $C$ a nonempty convex weak* compact subset of $E$. Let $G$ be a group of weak* continuous linear isometries on $E$. Suppose that $g(C)\subset C$ for all $g\in G$. ...
1
vote
2answers
1k views

Group action, Fixed point set and Orbit Space

I want to know to what extent is the group action determined by its fixed point data and orbit data, i.e. if $G$ acts on $M$ in two ways with the same fixed point set and orbit space, on what ...
8
votes
3answers
521 views

Is every (finite) group action on R^n by diffeomorphisms conjugate to a linear action?

I want to know if every smooth (finite)group action on $\mathbb{R}^n$ is conjugate to some linear action.Thank you!