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http://hdl.handle.net/11375/13384
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DC Field | Value | Language |
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dc.contributor.advisor | Hambleton, Ian | en_US |
dc.contributor.author | Anvari, Nima | en_US |
dc.date.accessioned | 2014-06-18T17:03:46Z | - |
dc.date.available | 2014-06-18T17:03:46Z | - |
dc.date.created | 2013-08-31 | en_US |
dc.date.issued | 2013-10 | en_US |
dc.identifier.other | opendissertations/8204 | en_US |
dc.identifier.other | 9187 | en_US |
dc.identifier.other | 4534349 | en_US |
dc.identifier.uri | http://hdl.handle.net/11375/13384 | - |
dc.description.abstract | <p>Let $p>5$ be a prime and $X_0$ a simply-connected $4$-manifold with boundary the Poincar\'e homology sphere $\Sigma(2,3,5)$ and even negative-definite intersection form $Q_{X_0}=\text{E}_8$ . We obtain restrictions on extending a free $\bZ/p$-action on $\Sigma(2,3,5)$ to a smooth, homologically-trivial action on $X_0$ with isolated fixed points. It is shown that for $p=7$ there is no such smooth extension. As a corollary, we obtain that there does not exist a smooth, homologically-trivial $\bZ/7$-equivariant splitting of $\#^8 S^2 \times S^2=E_8 \cup_{\Sigma(2,3,5)} \overline{E_8}$ with isolated fixed points. The approach is to study the equivariant version of Donaldson-Floer instanton-one moduli spaces for $4$-manifolds with cylindrical ends. These are $L^2$-finite anti-self dual connections which asymptotically limit to the trivial product connection.</p> | en_US |
dc.subject | group actions | en_US |
dc.subject | four-manifolds | en_US |
dc.subject | gauge theory | en_US |
dc.subject | Geometry and Topology | en_US |
dc.subject | Geometry and Topology | en_US |
dc.title | Equivariant Gauge Theory and Four-Manifolds | en_US |
dc.type | thesis | en_US |
dc.contributor.department | Mathematics and Statistics | en_US |
dc.description.degree | Doctor of Philosophy (PhD) | en_US |
Appears in Collections: | Open Access Dissertations and Theses |
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File | Size | Format | |
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fulltext.pdf | 1.47 MB | Adobe PDF | View/Open |
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