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dc.contributor.authorKettner, Michaelen_US
dc.date.accessioned2008-02-07T18:11:34Z
dc.date.available2008-02-07T18:11:34Z
dc.date.issued2007-08-22en_US
dc.identifier.urihttp://hdl.handle.net/1853/19704
dc.description.abstractIn this thesis, we consider semi-algebraic sets over a real closed field R defined by quadratic polynomials. Semi-algebraic sets of R^k are defined as the smallest family of sets in R^k that contains the algebraic sets as well as the sets defined by polynomial inequalities, and which is also closed under the boolean operations (complementation, finite unions and finite intersections). We prove new bounds on the topological complexity of semi-algebraic sets over a real closed field R defined by quadratic polynomials, in terms of the parameters of the system of polynomials defining them, which improve the known results. We conclude the thesis with presenting two new algorithms along with their implementations.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectBetti numberen_US
dc.subjectHomotopy typeen_US
dc.subjectQuadratic surfacesen_US
dc.subjectQuadratic polynomialsen_US
dc.subject.lcshGeometry, Algebraic
dc.subject.lcshAlgorithms
dc.titleAlgorithmic and topological aspects of semi-algebraic sets defined by quadratic polynomialsen_US
dc.typeDissertationen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMathematicsen_US
dc.description.advisorCommittee Chair: Basu, Saugata; Committee Member: Etnyre, John; Committee Member: Ghomi, Mohammad; Committee Member: Gonzalez-Vega, Laureano; Committee Member: Powers, Victoriaen_US


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