%0 Journal Article %T Spectral multiplicity and odd K-theory %A Ronald G. Douglas %A Jerome Kaminker %J Mathematics %D 2008 %I arXiv %X In this paper we begin a study of the space of unbounded self-adjoint Fredholm operators as a classifying space for K^{1}(X), with the goal of incorporating the information in the eigenspaces and eigenvalues of the operators. In particular, the role that the multiplicity of eigenvalues plays is developed here. %U http://arxiv.org/abs/0801.2815v2