dc.contributor.advisor | Lee, Kyung-Bai | |
dc.contributor.author | Thuong, Scott Van | |
dc.date.accessioned | 2014-05-07T15:47:40Z | |
dc.date.available | 2014-05-07T15:47:40Z | |
dc.date.issued | 2014 | |
dc.identifier.uri | https://hdl.handle.net/11244/10360 | |
dc.description.abstract | Crystallographic 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.language | en | en_US |
dc.subject | Mathematics. | en_US |
dc.title | Classification, Cobordism, and Curvature of Four-Dimensional Infra-Solvmanifolds | en_US |
dc.contributor.committeeMember | Jablonski, Michael | |
dc.contributor.committeeMember | Shankar, Krishnan | |
dc.contributor.committeeMember | Walschap, Gerard | |
dc.contributor.committeeMember | Hahn, Sowon | |
dc.date.manuscript | 2014 | |
dc.thesis.degree | Ph.D. | en_US |
ou.group | College of Arts and Sciences::Department of Mathematics | |