Gregory R. Conner

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For n ≥ 0, we exhibit CAT(0) groups that are n-connected at infinity , and have boundary which is (n − 1)-connected, but this boundary has non-trivial n th-homotopy group. In particular, we construct 1-ended CAT(0) groups that are simply connected at infinity, but have a boundary with non-trivial fundamental group. Our base examples are 1-ended CAT(0)(More)
A subgroup Q of a group G is commensurated if the commensurator of Q in G is the entire group G. Our main result is that a finitely generated group G containing an infinite, finitely generated, commensurated subgroup H, of infinite index in G is 1-ended and semistable at ∞. If additionally, Q and G are finitely presented and either Q is 1-ended or the pair(More)
If G is a group, then subgroups A and B are commensurable if A ∩ B has finite index in both A and B. The commensurator of A in G, denoted Comm G (A), is {g ∈ G|(gAg −1) ∩ A has finite index in both A and gAg −1 }. It is straightforward to check that Comm G (A) is a subgroup of G. A subgroup A is commensurated in G if Comm G (A) = G. The central-izer of A in(More)
Two natural questions are answered in the negative: • " If a space has the property that small nulhomotopic loops bound small nulhomotopies, then are loops which are limits of nulhomotopic loops themselves nulhomotopic? " • " Can adding arcs to a space cause an essential curve to become nulho-motopic? " The answer to the first question clarifies the(More)
22 male American and 24 male French college students' knowledge of AIDS scores were equivalent on a currently constructed 18-item questionnaire. Both groups answered more than 75% of the questions correctly. The American students' homophobic bias and reaction scores were higher than those of the French students on a 43-item homophobic questionnaire. The(More)
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