Spectral Multiplicity and Odd K-Theory ,   Ronald G. Douglas,   Texas A & M University,  Wed, 24 March, 2010,   3:30 p.m. A-227


Following the introduction of topological K-theory by Atiyah and Hirzebruch about fifty years ago, Atiyah and Janich established generalization for cycles in the even group as families of Fredholm operators. Shortly thereafter, Atiyah and Singer did the same for cycles in the odd group using families of self-adjoint Fredholm operators. While the calculation of the Chern classes in this realization in the even case is standard, that is not true for the odd case.

In recent joint work with Kaminker, this question is investigated in the context of unbounded self-adjoint Fredholm operators with compact resolvents with strong assumptions on the multiplicity of eigenvalues of the operators. In this talk I will describe some preliminary results along with some questions and relations to other work.