In this thesis, we set up a framework to define knot invariants for each choice of a symmetric space. In order to address this task, we start by defining appropriate notions of singular bundles and singular connections for a given symmetric space. We can associate a moduli space to any singular bundle defined over a compact 4-manifold with possibly non-empty boundary. We study these moduli spaces and show that they enjoy nice properties. For example, in the case of the symmetric space SU(n)/SO(n) the moduli space can be perturbed to an orientable manifold. Although this manifold is not necessarily compact, we introduce a comapctification of it. We then use this moduli space for singular bundles defined over 4-manifolds of the form YxR to define knot invariants. In another direction we mimic the construction of Donaldson invariants to define polynomial invariants for closed 4-manifolds equipped with smooth action of Z/2Z. / Mathematics
| Identifer | oai:union.ndltd.org:harvard.edu/oai:dash.harvard.edu:1/12274589 |
| Date | January 2014 |
| Creators | Daemi, Aliakbar |
| Contributors | Kronheimer, Peter Benedict |
| Publisher | Harvard University |
| Source Sets | Harvard University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Rights | closed access |
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