Flat Bundles and Grassmann Framings

          @misc{ scivideos_PIRSA:12050025,
            doi = {10.48660/12050025},
            url = {https://pirsa.org/12050025},
            author = {Hurtubise, Jacques},
            keywords = {Mathematical physics},
            language = {en},
            title = {Flat Bundles and Grassmann Framings},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2012},
            month = {may},
            note = {PIRSA:12050025 see, \url{https://scivideos.org/index.php/pirsa/12050025}}
          }
          

Abstract

When considering flat unitary bundles on a punctured Riemann surface, it is often convenient to have a space that includes all possible holonomies around the punctures; such a space is provided by the extended moduli space of Jeffrey. On the other hand, there are certain inconveniences, in particular no clear link to complex geometry via a Narasimhan-Seshadri type theorem. It turns out that the situation can be remedied quite nicely by considering bundles with framings taking values in a Grassmannian. Analogs for general structure groups, and in particular links with recent work of Martens and Thaddeus, will also be discussed. (This is joint work with U. Bhosle and I. Biswas.)