We compute the Bieri-Neumann-Strebel-Renz geometric invariants, Σn, of the lamplighter groups Lm by using the Diestel-Leader graph DL(m,m) to represent the Cayley graph of Lm.

Author Bio

I am a mathematics major with a physics minor at the University of Maine at Farmington. This work was completed during the 2009-2010 academic year under the direction of Dr. Nicholas Koban with funding from the mathematics department and a Wilson Scholarship. I will graduate from the University of Maine at Farmington in May of 2010 with a Bachelor of Arts in Mathematics and will attend the graduate program at SUNY Binghamton where I will work toward a PhD in Mathematics. Outside of my mathematical pursuits I enjoy kayaking and playing guitar.