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.