# Jens Kaad (Trieste): "Joint torsion line bundles of commuting operators"

Jens Kaad (Trieste), will give a talk with title "Joint torsion line bundles of commuting operators"

Abstract:

In this talk I’ll associate a holomorphic line bundle to any commuting tuple of bounded operators on a Hilbert space. The transition functions for this bundle are given by the joint torsion which compares determinants of Fredholm complexes. The joint torsion is an invariant of the second algebraic K-group of the Calkin algebra (bounded operators modulo trace class operators). The main step is to prove that the transition functions for the joint torsion line bundle are indeed holomorphic. This is carried out by studying the Quillen-Freed holomorphic determinant line bundle over the space of Fredholm complexes. In particular I will construct a holomorphic section of a certain pull-back of this bundle. The talk is based on joint work with Ryszard Nest.