(Georgia Institute of Technology, 2021-08-18)
Min, Hyun Ki
One of important problems in 3-dimensional contact geometry is to figure out which 3-manifolds admit tight contact structures and classify tight contact structures on the manifolds which admit tight contact structures. It turned out that this problem is closely related to the topology of 3-manifolds. For Seifert fibered spaces and toroidal manifolds, there has been a lot of results. On the other hand, there has been relatively few results for hyperbolic manifolds. In this thesis, we classify tight contact structures on the Weeks manifold, which is a hyperbolic L-space, having the smallest volume among all closed orientable hyperbolic 3-manifolds.