# Metric properties of Houghton's groups

José Burillo
Universitat Politècnica de Catalunya
27 February 2013, 12 noon - 1pm, AGR or Carslaw 451, University of Sydney

## Abstract

Houghton groups were defined in the 1960s, and provided examples of groups which belong to class $$FP_n$$ but not to class $$FP_{n+1}$$. Recently these groups have been studied from the modern geometric point of view. I will present here some results related to Houghton's groups: find an estimate for their metric, find their automorphism group and their commensurator group, proving that it is infinitely generated. As it embeds into the quasi-isometry group, this provides a large quantity of examples of quasi-isometries of Houghton's groups.