Metrics of positive scalar curvature and generalised Morse functions

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dc.contributor.authorWalsh, Mark, 1976-
dc.date.accessioned2010-03-12T01:15:37Z
dc.date.available2010-03-12T01:15:37Z
dc.date.issued2009-06
dc.descriptionx, 164 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.en_US
dc.description.abstractWe study the topology of the space of metrics of positive scalar curvature on a compact manifold. The main tool we use for constructing such metrics is the surgery technique of Gromov and Lawson. We extend this technique to construct families of positive scalar curvature cobordisms and concordances which are parametrised by Morse functions and later, by generalised Morse functions. We then use these results to study concordances of positive scalar curvature metrics on simply connected manifolds of dimension at least five. In particular, we describe a subspace of the space of positive scalar curvature concordances, parametrised by generalised Morse functions. We call such concordances Gromov-Lawson concordances. One of the main results is that positive scalar curvature metrics which are Gromov-Lawson concordant are in fact isotopic. This work relies heavily on contemporary Riemannian geometry as well as on differential topology, in particular pseudo-isotopy theory. We make substantial use of the work of Eliashberg and Mishachev on wrinkled maps and of results by Hatcher and Igusa on the space of generalised Morse functions.en_US
dc.description.sponsorshipCommittee in charge: Boris Botvinnik, Chairperson, Mathematics; James Isenberg, Member, Mathematics; Hal Sadofsky, Member, Mathematics; Christopher Phillips, Member, Mathematics; Michael Kellman, Outside Member, Chemistryen_US
dc.identifier.urihttps://hdl.handle.net/1794/10265
dc.language.isoen_USen_US
dc.publisherUniversity of Oregonen_US
dc.relation.ispartofseriesUniversity of Oregon theses, Dept. of Mathematics, Ph. D., 2009;
dc.subjectScalar curvatureen_US
dc.subjectMorse functionsen_US
dc.subjectConcordancesen_US
dc.subjectWrinkled mapsen_US
dc.subjectMathematicsen_US
dc.titleMetrics of positive scalar curvature and generalised Morse functionsen_US
dc.typeThesisen_US

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