Magnus subgroups of one-relator surface groups

A one-relator surface group is the quotient of an orientable surface group by the normal closure of a single relator. A Magnus subgroup is the fundamental group of a suitable incompressible sub-surface. A number of results are proved about the intersections of such subgroups and their conjugates, analogous to results of Bagherzadeh, Brodskii, and Collins in classical one-relator group theory.Comment: 15 pages, 3 figure

Boundary slopes of some non-Montesinos knots

It is shown that there exist alternating non-Montesinos knots whose essential spanning surfaces with maximal and minimal boundary slopes are not realised by the checkerboard surfaces coming from a reduced alternating planar diagram.Comment: 6 pages, 3 figure

Minimal Seifert manifolds for higher ribbon knots

We show that a group presented by a labelled oriented tree presentation in which the tree has diameter at most three is an HNN extension of a finitely presented group. From results of Silver, it then follows that the corresponding higher dimensional ribbon knots admit minimal Seifert manifolds.Comment: 33 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon1/paper12.abs.htm

Us, Them, and Me! Intergroup and personal challenges of aging successfully

This Keynote Address was delivered at the 73 rd . Annual New York State Communication Association Conference on October 16, 2015. After an anecdotal foray into how he came to study “geronto-communication”, Dr. Giles reviewed his and others’ research and theory on the interfaces between intergenerational communication, subjective health, and aging across many Western and Asian settings. This programmatic body of work was, in large part, guided by communication accommodation theory (which was briefly overviewed). Thereafter, Dr. Giles introduced various views of successful aging and the role of communication practices therein. This led to the formulation and testing of a new theoretical framework, the communication ecology model of successful aging. The thrust of this work is even more poignant as lifespan boundaries and expectations are being incrementally extended

Can Dehn surgery yield three connected summands?

A consequence of the Cabling Conjecture of Gonzalez-Acu\~{n}a and Short is that Dehn surgery on a knot in $S^3$ cannot produce a manifold with more than two connected summands. In the event that some Dehn surgery produces a manifold with three or more connected summands, then the surgery parameter is bounded in terms of the bridge number by a result of Sayari. Here this bound is sharpened, providing further evidence in favour of the Cabling Conjecture.Comment: 11 pages, 2 figure

The Tits alternative for generalized triangle groups of type (3, 4, 2)

A generalized triangle group is a group that can be presented in the form G = h x, y | xp = yq = w(x, y)r = 1 i where p, q, r ? 2 and w(x, y) is a cyclically reduced word of length at least 2 in the free product Zp ? Zq = h x, y | xp = yq = 1i. Rosenberger has conjectured that every generalized triangle group G satisfies the Tits alternative. It is known that the conjecture holds except possibly when the triple (p, q, r) is one of (2, 3, 2), (2, 4, 2), (2, 5, 2), (3, 3, 2), (3, 4, 2), or (3, 5, 2). Building on a result of Benyash-Krivets and Barkovich from this journal, we show that the Tits alternative holds in the case (p, q, r) = (3, 4, 2)