# Seminar of Algebra

### Homeomorphism groups of cubes and other $n$-manifolds

Speaker:
Dale Rolfsen (University of British Columbia and Pacific Institute for the Mathematical Sciences)
Email:
rolfsen@math.ubc.ca
Location:
Departamento de Álgebra
Date:
Thu, 4 feb 2016 12:00
Research interests include topology and algebra with recent emphasis on geometric group theory and orderable groups.

Let $I^n$ denote the unit n-dimensional cube. In joint work with Danny Calegari, we show that the group of piecewise-linear homeomorphisms of $I^n$, fixed on the boundary, is locally indicable and therefore left-orderable. The same is true more generally for PL manifolds with boundary. Similar results apply in the $C^{\infty}$ category but not in the topological category. Locally indicable means that every nontrivial finitely-generated subgroup has an infinite cyclic quotient, and a group is left-orderable if its elements enjoy a strict total ordering which is preserved under left-multiplication.