Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Alan Carey (Australian National University, Canberra)
When applied to condensed matter theory, the spectral flow for paths in the space of skew adjoint Fredholm operators suggests that we consider a generalisation that encompasses all of the classifying spaces for real K theory (ie the KO spectra) and not just the very first one (the skew adjoint Fredholm operators).
We build on the paper of Atiyah-Singer on index theory for skew adjoint Fredholm operators. Simply stated, their paper realises the homotopy groups \pi_0 for the KO classifying spaces as an analytic index whereas we focus on the group \pi_1 that is naturally associated with spectral flow.