论文标题
同态非伴形歧管同态组的自动连续性
Automatic continuity for homeomorphism groups of noncompact manifolds
论文作者
论文摘要
我们将歧管同构基团的自动连续性证明扩展到具有标记点及其映射类组的非紧密歧管和歧管。具体来说，我们表明，对于任何歧管$ m $同质形态，对紧凑型歧管的内部以及$ x \ subset m $同型同型与康托尔集和有限套件的结合，相对同型组$ \ mathrm {homeo}（homeo}（homeo}） x）/\ mathrm {homeo} _0（m，x）$具有从这样的组到任何可分离拓扑组的任何同构的属性，都一定是连续的。
We extend the proof of automatic continuity for homeomorphism groups of manifolds to non-compact manifolds and manifolds with marked points and their mapping class groups. Specifically, we show that, for any manifold $M$ homeomorphic to the interior of a compact manifold, and a set $X \subset M$ homeomorphic to the union of a Cantor set and finite set, the relative homeomorphism group $\mathrm{Homeo}(M, X)$ and the mapping class group $\mathrm{Homeo}(M, X)/\mathrm{Homeo}_0(M,X)$ have the property that any homomorphism from such a group to any separable topological group is necessarily continuous.
