Ross Geoghegan

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Given a set S equipped with a binary operation (we call this a “bracket algebra”) one may ask to what extent the binary operation satisfies some of the consequences of the associative law even when it is not actually associative? We define a subgroup Assoc(S) of Thompson’s Group F for each bracket algebra S, and we interpret the size of Assoc(S) as(More)
!i h ABSTRACT. Let Xx <— X2 <— ■ • • be an inverse sequence of spaces and maps satisfying (i) each Xn has the homotopy type of a CW complex, (ii) each fn is a Hurewicz fibration, and (iii) the connectivity of the fiber of fn goes to 00 with n. Let X be the inverse limit of the sequence. It is shown that the natural homomorphism Hk(X, G) —> Hk(X, G) (from(More)
This paper is about geometric and topological properties of a proper CAT(0) spaceX which is cocompact i.e. which has a compact generating domain with respect to the full isometry group. It is shown that geodesic segments in X can “almost” be extended to geodesic rays. A basic ingredient of the proof of this geometric statement is the topological theorem(More)
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(More)
The relationship between xed point theory and K {theory is explained, both classical Nielsen theory (versus K 0) and 1{parameter xed point theory (versus K 1). In particular, various zeta functions associated with suspension ows are shown to come in a natural way as \traces" of \torsions" of Whitehead and Reidemeister type.