The L2-Alexander invariant for knots and links
Date of Issue2017-12-08
School of Physical and Mathematical Sciences
This thesis focuses on the computation of L2 invariants. The first part is on the L2-Alexander invariant for knots and links. One presents the construction of this invariant, followed by its well known properties. In particular, one shows how to compute this invariant using deficiency 1 presentations, and also that this invariant detects the unknot. The second part gives explicit computations of the spectral density function of right multiplication operators arising from groups that are known to be virtually free. Finally, one presents a new proof of the pointwise a.e. convergence of the spectral density functions for for right multiplication operators R_w : l_2G -> l_2G.