The projective Dirac operator and its Fractional Analytic Index

10 June 2005
I will give an expository account of Mathai, Melrose, and Singer [math.DG/0402329], explaining how to define the projective Dirac &quot;operator&quot; when the underlying manifold is neither spin nor spin_C, and how to define its analytic index which need not be an integer. Nevertheless, the usual index formulas apply. <i>Professor Singer will be admitted as honorary member of the London Mathematical Society just before his talk.</i>