Almost linear actions by finite groups on S^{2n-1}

Almost complex circle actions with few fixed points

We show that almost complex circle actions with exactly three fixed points do not exist in dimension 8 and present an infinite series of 6-dimensional manifolds possessing an almost complex circle action with exactly two fixed points.

具有几乎指定局部作用的树作用群的的有界上同调

Bounded cohomology of groups acting on trees with almost prescribed local actions

本文研究了具有几乎指定局部作用的树作用群的有界上同调，证明了当有限置换群为2-传递时其有界上同调消失，否则实系数二阶有界上同调为无限维。

Topological models of finite type for tree almost automorphism groups

We show that tree almost automorphism groups, including Neretin groups, satisfy the analogue of the $F_\infty$-finiteness condition in the world of totally disconnected groups: They possess a cellular action on a contractible cellular complex such that the stabilizers are open and compact and the restriction of the action on each $n$-skeleton is cocompact.

Mapping classes are almost determined by their finite quotient actions

Given any connected compact orientable surface, a pair of mapping classes are said to be procongruently conjugate if they induce a conjugate pair of outer automophisms on the profinite completion of the fundamental group of the surface. For example, this occurs if they induce conjugate outer automorphisms on every characteristic finite quotient of the fundamental group. In this paper, it is shown that every procongruent conjugacy class of mapping classes, as a subset of the surface mapping class group, is the disjoint union of at most finitely many conjugacy classes of mapping classes. For any…

Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups

For any orientable finite-volume hyperbolic 3-manifold, this paper proves that the profinite isomorphism type of the fundamental group uniquely determines the isomorphism type of the first integral cohomology, as marked with the Thurston norm and the fibered classes; moreover, up to finite ambiguity, the profinite isomorphism type determines the isomorphism type of the fundamental group, among the class of finitely generated 3-manifold groups.

Almost fixed points of finite group actions on manifolds without odd cohomology

If $X$ is a smooth manifold and ${\mathcal{G}}$ is a subgroup of $Diff(X)$ we say that $(X,{\mathcal{G}})$ has the almost fixed point property if there exists a number $C$ such that for any finite subgroup $G\leq{\mathcal{G}}$ there is some $x\in X$ whose stabilizer $G_x\leq G$ satisfies $[G:G_x]\leq C$. We say that $X$ has no odd cohomology if its integral cohomology is torsion free and supported in even degrees. We prove that if $X$ is compact and possibly with boundary and has no odd cohomology then $(X,Diff(X))$ has the almost fixed point property. Combining this with a result of Petrie an…