史恩慧: Topological and algebraic obstructions for distal minimal group actions on continua

：史恩慧 教授

We study the topological characters of a continuum $X$ and the algebraic structures of a group $G$ that forbid $G$ from acting on $X$ distally and minimally. Explicitly, we obtain the following results: (1)  Let $G$ be a lattice in ${\rm SL}(n, \mathbb R)$ with $n\geq 3$ and $\mathcal S$ be a closed surface. Then $G$ has no distal minimal action on $\mathcal S$. (2) If $X$ admits a distal minimal action by a finitely generated amenable group, then the first \v Cech cohomology group ${\check H}^1(X)$ with integer coefficients is nontrivial. In particular, if $X$ is homotopically equivalent to a CW complex, then $X$ cannot be simply connected.