Flat Bundles and Grassmann Framings


Hurtubise, J. (2012). Flat Bundles and Grassmann Framings. Perimeter Institute. https://pirsa.org/12050025


Hurtubise, Jacques. Flat Bundles and Grassmann Framings. Perimeter Institute, May. 06, 2012, https://pirsa.org/12050025


          @misc{ pirsa_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},
            year = {2012},
            month = {may},
            note = {PIRSA:12050025 see, \url{https://pirsa.org}}

Jacques Hurtubise McGill University


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.)