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Full-Text Articles in Physical Sciences and Mathematics
Obstructions To Embedding Genus-1 Tangles In Links, Susan Marie Abernathy
Obstructions To Embedding Genus-1 Tangles In Links, Susan Marie Abernathy
LSU Doctoral Dissertations
Given a compact, oriented 3-manifold M in S3 with boundary, an (M,2n)-tangle T is a 1-manifold with 2n boundary components properly embedded in M. We say that T embeds in a link L in S3 if T can be completed to L by adding a 1-manifold with 2n boundary components exterior to M. The link L is called a closure of T. We focus on the case of (S_1 x D_2, 2)-tangles, also called genus-1 tangles, and consider the following question: given a genus-1 tangle G and a link L, how can we tell if L is a closure of …
Invariants Of Legendrian Products, Peter Lambert-Cole
Invariants Of Legendrian Products, Peter Lambert-Cole
LSU Doctoral Dissertations
This thesis investigates a construction in contact topology of Legendrian submanifolds called the Legendrian product. We investigate and compute invariants for these Legendrian submanifolds, including the Thurston-Bennequin invariant and Maslov class; Legendrian contact homology for the product of two Legendrian knots; and generating family homology.