论文标题
单模型完全断开的本地紧凑型组的合理离散同胞维度一个
Unimodular totally disconnected locally compact groups of rational discrete cohomological dimension one
论文作者
论文摘要
结果表明，stallings-swan定理在完全断开的局部紧凑（= t.d.l.c.）上下文（参见thm。b）中。更确切地说，紧凑的$ \ Mathcal {Co} $ - 有限的T.D.L.C.理性离散的同胞尺寸小于或等于$ 1 $的组$ g $对于有限的涂鸦组的基本组是同构的。该结果概括了邓伍德（Dunwoody）的经典失速版的合理版本 - 宽度定理至T.D.L.C.组。定理B的证明是基于以下事实：紧凑的单型T.D.L.C.具有理性离散的同胞维度$ 1 $的组必然是非阳性的Euler-Poincaré特征（参见Thm。H）。
It is shown that a Stallings--Swan theorem holds in a totally disconnected locally compact (= t.d.l.c.) context (cf. Thm. B). More precisely, a compactly generated $\mathcal{CO}$-bounded t.d.l.c. group $G$ of rational discrete cohomological dimension less than or equal to $1$ must be isomorphic to the fundamental group of a finite graph of profinite groups. This result generalises Dunwoody's rational version of the classical Stallings--Swan theorem to t.d.l.c. groups. The proof of Theorem B is based on the fact that a compactly generated unimodular t.d.l.c. group with rational discrete cohomological dimension $1$ has necessarily non-positive Euler--Poincaré characteristic (cf. Thm. H).
