Peter Kropholler is Professor of Pure Mathematics at the University of Southampton. Ian Leary is Professor of Pure Mathematics at the University of Southampton. Conchita Martínez-Pérez is Professor of Pure Mathematics at the University of Zaragoza. Brita Nucinkis is Professor of Mathematics at Royal Holloway, University of London.

• Preface Peter H. Kropholler, Ian J. Leary, Conchita Martínez-Pérez and Brita E. A. Nucinkis; Obstructions for subgroups of Thompson's group V José Burillo, Sean Cleary and Claas E. Röver; Groups of homological dimension one Ioannis Emmanouil; Braided diagram groups and local similarity groups Daniel S. Farley and Bruce Hughes; On Thompson's group T and algebraic K-theory Ross Geoghegan and Marco Varisco; Special cube complexes Robert Kropholler; A hyperbolic group with a finitely presented subgroup that is not of type FP3 Yash Lodha; The structure of euclidean Artin groups Jon McCammond; Finitely presented groups associated with expanding maps Volodymyr Nekrashevych; On characteristic modules of groups Olympia Talelli; Controlled algebra for simplicial rings and algebraic K-theory Mark Ullmann.