Published Papers

• Bibliography of Published Work to December 2020

Preprints



• The complexity of balanced presentations and the Andrews-Curtis conjecture.



• Profinite rigidity, fibering, and the figure-eight knot.
(with A.W. Reid; to appear in volume dedicated to Bill Thurston)


• The strong profinite genus of a finitely presented group can be infinite
(to appear in JEMS)


• Cube complexes, subgroups of mapping class groups, and nilpotent genera
(Notes based on Clay Lecture. To appear in IAS/PCMI volume on Geometric Group Theory and CMI volume ``Lectures on Geoemtry")



With Henry Wilton

• The triviality problem for profinite completions
(Inventiones)


• The isomorphism problem for profinite completions of residually finite groups
(Groups, Geometry & Dynamics)


• Decidability and the developablity of permutoids and rigid pseudogroups
(Sigma)


• On the recognition problem for virtually special cube complexes
(to appear in a volume of the Japan Math Soc)


With Dessilava Kochloukova

• The virtual first betti number of soluble groups
(Pacific Journal)


• Volume gradients and homology in towers of residually-free groups
(to appear in Math Ann)



With Alan Reid

• Nilpotent completions of groups, Grothendieck pairs, and four problems of Baumslag.
(IMRN)




New in 2012




• Determining Fuchsian groups by their finite quotients
(with Marston Conder and Alan Reid; to appear in Israel J)


• Dimension of elementary amenable groups.
(with Peter Kropholler; in Crelle)


• Actions of arithmetic groups on homology spheres and acyclic homology Manifolds.
(with F. Grunewald and K. Vogtmann; in Math Z)


• On the Subgroups of Right Angled Artin Groups and Mapping Class Groups.
(in Math Res Lett)


• On the finite presentation of subdirect products and the nature of residually free groups.
(with J. Howie. C.F. Miller, H.B. Short; in Amer J Math)



New or updated in 2011




• The rhombic dodecahedron and semisimple actions of Aut(F_n) on CAT(0) spaces



• On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups
(with Lawrence Reeves)



• New in 2010

  
  
  
• The Dehn functions of Out(F_n) and Aut (F_n)
(with Karen Vogtmann)


• On the difficulty of presenting finitely presentable groups
(with Henry Wilton)


• Abelian covers of graphs and maps between outer automorphism groups of free groups
(with Karen Vogtmann)


• Actions of higher-rank lattices on free groups
(with Richard D Wade)


• Cofinitely Hopfian groups, open mappings and knot complements
(with D.Groves, J.A.~Hillman, and G.J.~Martin)


New or updated in 2009




• Semisimple actions of mapping class groups on CAT(0) spaces.
  
  
• On the dimension of CAT(0) spaces where mapping class groups can act.
  
  

  New or updated in 2008

  
  
  
• Finitely presented residually free groups
(with Jim Howie, Chuck Miller and Hamish Short)


• The quadratic isoperimetric inequality for mapping tori
  of free-group automorphisms
(with Daniel Groves)
This 188 page memoir is the final account of our long-running project to prove the
theorem in the title. The final manuscript is a compilation of the three previous
papers by the same authors that are described below.


• Actions of automorphism groups of free groups on homology spheres and acyclic manifolds
(with Karen Vogtmann)


• Three papers on decision problems and profinite completions of groups



• The Chabauty space of closed subgroups of the three-dimensional Heisenberg group
(with Pierre de la Harpe and Victor Klepstyn)



New in 2007



• Infinite Groups with Fixed Point Properties
(with G.Arzhantseva, T.Januszkiewicz, I.J.Leary, A.Minasyan, J.Swiatkowski)


• Subgroups of Direct Products of Limit Groups
(with Jim Howie, Chuck Miller and Hamish Short)


• Structure and finiteness properties of subdirect products of groups
(with Chuck Miller)


• Subgroup separability in residually free groups
(with Henry Wilton)


• Constructing presentations of subgroups of right-angled Artin groups
(with Michael Tweedale)



My article for the proceedings of ICM2006

• Non-positive curvature and complexity for finitely presented groups





New in 2006

• The quadratic isoperimetric inequality for mapping tori
  of free-group automorphisms II: the general case
(with Daniel Groves)


• Snowflake groups, Perron-Frobenius eigenvalues, and isoperimetric spectra
(with Noel Brady, Max Forester, Krishnan Shankar)


• Deficiency and abelianized deficiency of some virtually free groups
(with Michael Tweedale)


• Quasiregular self-mappings of manifolds and word hyperbolic groups
(with Aimo Hinkkanen and Gaven Martin)


• A condition that prevents groups from acting non-trivially on trees




New in 2005

• Extrinsic versus intrinsic diameter for Riemannian filling discs and van Kampen diagrams

(with Tim Riley)


• Free and fragmenting filling length

(with Tim Riley)


• Subdirect products of two limit groups

(with Jim Howie)


• Free-group automorphisms, train tracks, and the Beaded Decomposition

(with Daniel Groves)


• Automorphisms groups of free, surface, and free abelian groups

(with Karen Vogtmann)


• Normalizers in Limit Groups

(with Jim Howie)


• Subgroups of direct products of elementarily free groups

(with Jim Howie)


• Lecture Notes from Cannonfest, Park City 2003



• Limit groups, positive-genus towers and measure equivalence

(with M.Tweedale and H.Wilton)





From 2003 and 2004

• Grothendieck's problems concerning profinite completions and representations of groups

(with Fritz Grunewald)


• Conjugacy of finite subsets in hyperbolic groups

(with James Howie)


• On the growth of groups and automorphisms



• Mapping Class Groups and Outer Automorphism Groups
  of Free Groups are C* Simple

(with Pierre de la Harpe)


• A note on the grammar of combings
  





New or updated in 2002

• The Quadratic Isoperimetric Inequality for
  Mapping Tori of Free-Group Automorphisms I: Positive Automorphisms

(with Daniel Groves)


• The Geometry of the Word Problem



• The conjugacy and isomorphism problems for combable groups



• Recognition of subgroups of direct products of hyperbolic groups

(with Chuck Miller)


• Homomorphisms from automorphism groups of free groups

(with Karen Vogtmann)

 

2001 or Earlier

• There is only one gap in the isoperimetric spectrum

(with Noel Brady)


• On the subgroups of semihyperbolic groups




• The Symmetries of Outer space

(with Karen Vogtmann)


• Combings of Groups and the Grammar of Reparameterisation




• Finiteness Properties for Subgroups of GL$(n,\Bbb Z)$




• Polynomial Dehn Functions and the Length of Asynchronously Automatic Structures




• Context-Free Languages of Sub-Exponential Growth

(with Bob Gilman)


• The Automorphisms of Automorphism Groups of Free Groups

(with Karen Vogtmann)


• Length Functions, Curvature and the Dimension of Discrete Groups




• A Remark About Actions of Lattices on Free Groups

(with Benson Farb)


• The Subgroups of Direct Products of Surface Groups

(with Jim Howie, Chuck Miller and Hamish Short)


• Finite presentation of fibre products of metabelian groups

(with Gilbert Baumslag, Derek Holt and Chuck Miller)

My PhD Thesis

• Geodesics and curvature in metric simplicial complexes
This is a large file (4MB) because it is a scan.