3 N ov 1 99 8 Connectivity properties of group actions on non - positively curved spaces I : Controlled connectivity and openness results
نویسنده
چکیده
A thorough outline of this paper is given in §2. In this introduction we give a quick indication of what the paper and (to some extent) its sequel [BGII] are about. Let G be a group of type Fn, let (M, d) be a simply connected proper “nonpositively curved” (i.e. CAT(0)) metric space, and let ρ : G → Isom(M) be an action of G onM by isometries. We introduce a topological property called (uniform) “controlled (n − 1)-connectedness”, abbreviated to CC, which such an action ρ may or may not possess. This property is extracted and generalized from work on the “geometric invariants Σ(G) of the group G (e.g. [BS 80], [BNS 87], [BRe 88], [Re 88, 89], [BS]) which applies in the special case where M = IE and ρ is an action by translations. Experience with this special case suggests that CC is a fundamental property, and we are encouraged in this belief by two instances in which CC turns out to be equivalent to something familiar:
منابع مشابه
3 N ov 1 99 8 Connectivity properties of group actions on non - positively curved spaces II : The geometric invariants
This Part II continues our paper [BGI], but we have made it as independent of that paper as possible. The reader familiar with the self-contained essay on finitary sheaves and finitary maps which is §4 of [BGI] can read this second paper with occasional references back to [BGI] for some details and analogies. A full outline of the present paper is found in §10 below. Let G be a group, let M be ...
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