06.06.2023, 15 Uhr
Phenomena in High Dimensions
Pierre Youssef (New York University, Abu Dhabi)
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.