10 papers
Finiteness Properties of Locally Defined Groups
Daniel S. Farley, Bruce Hughes
Let be a set and let be an inverse semigroup of partial bijections of . Thus, an element of is a bijection between two subsets of , and the set is required to…
Braided Diagram Groups and Local Similarity Groups
Daniel Farley, Bruce Hughes
Hughes defined a class of groups that act as local similarities on compact ultrametric spaces. Guba and Sapir had previously defined braided diagram groups over semigroup presentat…
Finiteness properties of some groups of local similarities
Daniel S. Farley, Bruce Hughes
Hughes has defined a class of groups, which we call FSS (finite similarity structure) groups. Each FSS group acts on a compact ultrametric space by local similarities. The best-kno…
Bounded distortion homeomorphisms on ultrametric spaces
Bruce Hughes, Álvaro Martínez-Pérez, Manuel A. Morón
It is well-known that quasi-isometries between R-trees induce power quasi-symmetric homeomorphisms between their ultrametric end spaces. This paper investigates power quasi-symmetr…
Dihedral manifold approximate fibrations over the circle
Bruce Hughes, Qayum Khan
Consider the cyclic group C_2 of order two acting by complex-conjugation on the unit circle S^1. The main result is that a finitely dominated manifold W of dimension > 4 admits a c…
Local similarities and the Haagerup property
Bruce Hughes
A new class of groups, the locally finitely determined groups of local similarities on compact ultrametric spaces, is introduced and it is proved that groups in this class have the…