Involutions with n-Dimensional Fixed-Sets.
We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.
We construct a variant of Karoubi’s relative Chern character for smooth varieties over and prove a comparison result with Beilinson’s regulator with values in Deligne-Beilinson cohomology. As a corollary we obtain a new proof of Burgos’ Theorem that for number fields Borel’s regulator is twice Beilinson’s regulator.