Ross Geoghegan

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The Product Conjecture for the homological Bieri-Neumann-Strebel-Renz invariants is proved over a field. Under certain hypotheses the Product Conjecture is shown to also hold over Z, even though D. Schütz has recently shown that the Conjecture is false in general over Z. Our version over Z is applied in a joint paper with D. Kochloukova [5] to show that for(More)
Thompson's group F is the group of all increasing dyadic PL homeomorphisms of the closed unit interval. We compute Σ m (F) and Σ m (F ; Z), the homotopical and homological Bieri-Neumann-Strebel-Renz invariants of F , and show that Σ m (F) = Σ m (F ; Z). As an application, we show that, for every m, F has subgroups of type F m−1 which are not of type F Pm(More)
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)