Alexandroff Manifolds and Homogeneous Continua

Canadian mathematical bulletin

A. Karassev²  V. Todorov¹  V. Valov² 

[1] Department of Mathematics, UACG, Sofia, Bulgaria;Department of Computer Science and Mathematics, Nipissing University, North Bay, ON, P1B 8L7

关键词: Cantor manifold;    cohomological dimension;    cohomology groups;    homogeneous compactum;    separator;    $V^n$-continuum;   

DOI  :  10.4153/CMB-2013-010-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

ny homogeneous,metric $ANR$-continuum is a $V^n_G$-continuum provided $dim_GX=ngeq1$ and $check{H}^n(X;G)eq 0$, where $G$ is a principal idealdomain. This implies that any homogeneous $n$-dimensional metric $ANR$-continuum is a $V^n$-continuum in the sense of Alexandroff.We also prove that any finite-dimensional homogeneous metric continuum$X$, satisfying $check{H}^n(X;G)eq 0$ for some group $G$ and $ngeq1$, cannot be separated by a compactum $K$ with $check{H}^{n-1}(K;G)=0$ and $dim_G Kleqn-1$. This provides a partial answer to a question ofKallipoliti-Papasoglu whether any two-dimensional homogeneous Peano continuum cannot be separated by arcs.

【 授权许可】

Unknown