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http://hdl.handle.net/11375/13384
Title: | Equivariant Gauge Theory and Four-Manifolds |
Authors: | Anvari, Nima |
Advisor: | Hambleton, Ian |
Department: | Mathematics and Statistics |
Keywords: | group actions;four-manifolds;gauge theory;Geometry and Topology;Geometry and Topology |
Publication Date: | Oct-2013 |
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> |
URI: | http://hdl.handle.net/11375/13384 |
Identifier: | opendissertations/8204 9187 4534349 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Size | Format | |
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fulltext.pdf | 1.47 MB | Adobe PDF | View/Open |
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