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http://hdl.handle.net/11375/7073
Title: | Finite Group Actions on Smooth 4-Manifolds with Indefinite Intersection Form |
Authors: | Klemm, Michael |
Advisor: | Hambleton, I. |
Department: | Mathematics |
Keywords: | Mathematics;Mathematics |
Publication Date: | May-1995 |
Abstract: | <p>In this thesis finite cyclic group actions on S² x S² and its moduli space of anti-self-dual connections will be investigated. In the first step the equivariant version of the Donaldson gluing construction of anti-self-dual connections will be developed. We obtain an equivariant obstruction map which provides an equivariant local model of the anti-self-dual moduli space. Then we investigate the special case when we glue the product connection on a trivial SU(2)-bundle over S² x S² with two concentrated anti-instantons. We can achieve transversality of the obstruction map by an equivariant perturbation of the conformal class. We obtain a 10-dimensional equivariant local model which is diffeomorphic to R⁸ x R X S¹. The action on R⁸ is the direct sum of the isotropy representations. The action on the circle depends on the rotation numbers and the self-dual harmonic form. Moreover, there exists an equivariant perturbation of the conformal class so that there are no reducible anti-self-dual connections over S² x S² besides the trivial product connection. These results can be used to show that under certain assumptions the rotation numbers of the isotropy representations of a finite cyclic, smooth action on S² x S² coincide with those of some linear action.</p> |
URI: | http://hdl.handle.net/11375/7073 |
Identifier: | opendissertations/2369 3361 1375916 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Size | Format | |
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fulltext.pdf | 1.56 MB | Adobe PDF | View/Open |
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