Ross Geoghegan

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This paper is about geometric and topological properties of a proper CAT(0) space X 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)
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 As-soc(S) of Thompson's Group F for each bracket algebra S, and we interpret the size of Assoc(S) as(More)
In " zero-parameter " or classical Nielsen fixed point theory one studies Fix(f) := {x ∈ X | f (x) = x} where f : X → X is a map. In case X is an oriented compact manifold and f is transverse to the identity map, id X , Fix(f) is a finite set each of whose elements carries a natural sign, ±1, the index of that fixed point. The set Fix(f) is partitioned into(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.