On linear groups over polynomial rings

Speaker: Matthias Wendt (Freiburg)

Time: 4.00 PM

Date: Thursday November 15th 2012

Location: Mathematics Seminar Room, Room AG 1.01, First Floor, Agriculture Building, UCD Belfield


In the talk I will discuss linear groups, in particular SL_3, over polynomial rings. Krstic and McCool established that the group SL_2(R[T]) has a rather complicated abelianization whenever the ring R is not a field. I will explain a similar result for SL_3(R[T]): if R is not a field, then there are infinitely many relations in SL_3(R[T]) which do not follow from commutator formulas. This implies that the so-called homotopy invariance for group homology fails for SL_3.

Series: K Theory, Quadratic Form and Number Theory Seminar Series