Can Dehn surgery yield three connected summands? (2009)
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...
ONE-RELATOR PRODUCTS INDUCED FROM GENERALIZED TRIANGLE GROUPS (2009)
Abstract. We study the quotient of a free product of groups by the normal closure of a word that is contained in a certain type of 2-generator subgroup, and hence can be expressed in the form of a...
FREIHEITSSATZE FOR ONE-RELATOR QUOTIENTS OF SURFACE GROUPS AND OF LIMIT GROUPS (2009)
Howie, James, Saeed, Muhammad Sarwar
Three versions of the Freiheitssatz are proved in the context of one-relator quotients of limit groups, where the latter are equipped with 1-acylindrical splittings over cyclic subgroups. These are...
Normalisers in limit groups (2008)
Martin R. Bridson, James Howie, S Γ ×···×γn
Let Γ be a limit group, S ⊂ Γ a subgroup, and N the normaliser of S. IfH1(S, Q) has finite Q-dimension, then S is finitely generated and either N/S is finite or N is abelian. This result has...
A remark on double cosets (2008)
If a soluble group $G$ contains two finitely generated abelian subgroups $A,B$ such that the number of double cosets $AgB$ is finite, then $G$ is shown to be virtually polycyclic.
Finitely presented residually free groups (2008)
Bridson, Martin R., Howie, James, Miller III, Charles F., Short, Hamish
We establish a general criterion for the finite presentability of subdirect products of groups and use this to characterize finitely presented residually free groups. We prove that, for all...
This short note was inspired by a question from Fico Gonzalez Acu~na: Question 1 If and are two closed curves (nonsimple, in general) on an orientable
On the abstract groups (3; n; p; 2) (2007)
x0. Introduction. The groups (m; n; p; q) = ha; b j a
W. A. Bogley, N. D. Gilbert, James Howie, Is Cockcroft A
In a study of the word problem for groups, R. J. Thompson considered a certain group F of self-homeomorphisms of the Cantor set and showed, among other things, that F is finitely presented. Using...
ONE-RELATOR PRODUCTS INDUCED FROM GENERALIZED TRIANGLE GROUPS (2007)
Abstract. We study the quotient of a free product of groups by the normal closure of a word that is contained in a certain type of 2-generator subgroup, and hence can be expressed in the form of a...
A short proof of a theorem of Brodski (2007)
A short proof, using graphs and groupoids, is given of Brodski's Theorem that torsion-free one-relator groups are locally indicable 1
Martin Edjvet, Nottingham Ng Rd, James Howie, Gerhard Rosenberger, Richard M. Thomas
Finite generalized tetrahedron groups with a high-power relator
( de Gruyter 1998 Free subgroups in groups of small de®ciency (2007)
The de®ciency of a ®nite group presentation P: hX j Ri is def…P † ˆjXj jRj, the di¨erence between the numbers of generators and de®ning relators. For a given ®nitely presented group G, the...
( de Gruyter 1998 Free subgroups in groups of small deciency (2007)
The deciency of a nite group presentation P: hX j Ri is defP jX j
Magnus subgroups of one-relator surface groups (2007)
Howie, James, Saeed, Muhammad Sarwar
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...
Freiheitss\"{a}tze for one-relator quotients of surface groups and of limit groups (2007)
Howie, James, Saeed, Muhammad Sarwar
Three versions of the Freiheitssatz are proved in the context of one-relator quotients of limit groups, where the latter are equipped with 1-acylindrical splittings over cyclic subgroups. These are...
Winding numbers and SU(2)-representations of knot groups (2007)
Given an abelian group $A$ and a Lie group $G$, we construct a bilinear pairing from $A\times\pi_1({\mathcal R})$ to $\pi_1(G)$, where $\mathcal R$ is a subvariety of the variety of representations...
Subgroups of direct products of limit groups (2007)
Bridson, Martin R, Howie, James, Miller III, Charles F, Short, Hamish
If $G_1,...,G_n$ are limit groups and $S\subset G_1\times...\times G_n$ is of type $\FP_n(\mathbb Q)$ then $S$ contains a subgroup of finite index that is itself a direct product of at most $n$ limit...
We prove the conjecture that any band sum of two or more knots, at least one of which is non-trivial, is non-trivial.
The Quotient of a Free Product of Groups by a Single High-Powered Relator (2006)
Let A, B be groups, and r ∈ A * B a cyclically reduced word of the form xUyU−l for some word U and letters x, y, where x2 = y3 = l. We call this form exceptional. If m = 4 or...
Intersections of Magnus subgroups and embedding theorems for cyclically presented groups (2006)
A Magnus subgroup of a one-relator group is the free subgroup freely generated by a proper subset of the generators. Two such subgroups can intersect in the obvious way or in a larger, exceptional...
The Tits alternative for generalized triangle groups of type (3,4,2) (2006)
Howie, James, Williams, Gerald
A generalized triangle group is a group that can be presented in the form $G = < x,y | x^p=y^q=w(x,y)^r=1>$, where $p,q,r\geq 2$ and $w(x,y)$ is a cyclically reduced word of length at least 2 in the...
A Short proof of a theorem of Brodskii (2006)
A short proof, using graphs and groupoids, is given of Brodskii's theorem that torsion-free one-relator groups are locally indicable.
Subgroups of direct products of two limit groups (2005)
Bridson, Martin R., Howie, James
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.
Subgroups of direct products of elementarily free groups (2005)
Bridson, Martin R, Howie, James
We exploit Zlil Sela's description of the structure of groups having the same elementary theory as free groups: they and their finitely generated subgroups form a prescribed subclass E of the...
Normalisers in Limit Groups (2005)
Bridson, Martin R, Howie, James
Let $\G$ be a limit group, $S\subset\G$ a subgroup, and $N$ the normaliser of $S$. If $H_1(S,\mathbb Q)$ has finite $\Q$-dimension, then $S$ is finitely generated and either $N/S$ is finite or $N$ is...
The Tits alternative for generalised tetrahedron groups (2005)
A generalised tetrahedron group is the colimit of a triangle of groups whose vertex groups are generalised triangle groups and whose edge groups are finite cyclic. We prove an improved Spelling...
A recent result of D. J. Collins states that the intersection of two Magnus subgroups in a one-relator group consists either just of the ‘obvious ’ intersection, or exceptionally of the free...
Finite Generalized Tetrahedron Groups with a High-Power Relator (2002)
Edjvet, M., Howie, James, Rosenberger, Gerhard, Thomas, Richard M.
Bestvina-Brady groups and the plus construction (1999)
A recent result of Bestvina and Brady [1], Theorem 8.7, shows that one of two outstanding questions has a negative answer: either there exists a group of cohomological dimension 2 and geometric...
Bestvina-Brady groups and the plus construction (1999)
A recent result of Bestvina and Brady [1], Theorem 8.7, shows that one of two outstanding questions has a negative answer: either there exists a group of cohomological dimension 2 and geometric...
Minimal Seifert manifolds for higher ribbon knots (1998)
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...
Minimal seifert manifolds for higher ribbon knots (1997)
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...
Minimal Seifert manifolds for higher ribbon knots (1997)
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...
Minimal seifert manifolds for higher ribbon knots (1997)
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 nitely presented group. From results of Silver, it then...