738 research outputs found
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
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 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
Non-triviality of some one-relator products of three groups
In this paper we study a group G which is the quotient of a free product of
three non-trivial groups by the normal closure of a single element. In
particular we show that if the relator has length at most eight, then G is
non-trivial. In the case where the factors are cyclic, we prove the stronger
result that at least one of the factors embeds in G.Comment: 21 pages, 3 figure
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
Subgroups of direct products of two limit groups
If S is a subgroup of a direct product of two limit groups, and S is of type
FP(2) over the rationals, then S has a subgroup of finite index that is a
direct product of at most two limit groups.Comment: 18 pages, no figure
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