Classification, Cobordism, and Curvature of Four-Dimensional Infra-Solvmanifolds

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dc.contributor.advisorLee, Kyung-Bai
dc.contributor.authorThuong, Scott Van
dc.contributor.committeeMemberJablonski, Michael
dc.contributor.committeeMemberShankar, Krishnan
dc.contributor.committeeMemberWalschap, Gerard
dc.contributor.committeeMemberHahn, Sowon
dc.date.accessioned2014-05-07T15:47:40Z
dc.date.available2014-05-07T15:47:40Z
dc.date.issued2014
dc.date.manuscript2014
dc.description.abstractCrystallographic groups of solvable Lie groups generalize the crystallographic groups of Euclidean space. The quotient of a solvable Lie group G by the action of a torsion-free crystallographic group of G is an infra-solvmanifold of G. Infra-solvmanifolds are aspherical manifolds that generalize both closed flat manifolds and closed almost flat manifolds (that is, infra-nilmanifolds). Here we complete the classification of 4-dimensional infra-solvmanifolds by classifying torsion-free crystallographic groups of certain 4-dimensional solvable Lie groups. The classification also includes those crystallographic groups with torsion. We prove that every 4-dimensional infra-solvmanifold is the boundary of a compact 5-dimensional manifold by constructing an involution on certain 4-dimensional infra-solvmanifolds which is either free, or has 2-dimensional fixed set. The Ricci signatures (that is, signatures of the Ricci transformation) of 4-dimensional Lie groups have been classified. A Ricci signature can be realized on an infra-solvmanifold M of G if M is a compact isometric quotient of G, where G has left invariant metric with prescribed Ricci signature. We classify which Ricci signatures can be realized on certain 4-dimensional infra-solvmanifolds.en_US
dc.identifier.urihttp://hdl.handle.net/11244/10360
dc.languageenen_US
dc.subjectMathematics.en_US
dc.thesis.degreePh.D.en_US
dc.titleClassification, Cobordism, and Curvature of Four-Dimensional Infra-Solvmanifoldsen_US
ou.groupCollege of Arts and Sciences::Department of Mathematics

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