Title:
Constructions and Invariants of High-Dimensional Legendrian Submanifolds
Constructions and Invariants of High-Dimensional Legendrian Submanifolds
Author(s)
Roy, Agniva
Advisor(s)
Etnyre, John B.
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Abstract
This thesis explores the question of understanding Legendrian submanifolds in contact manifolds of dimension greater than 3. There are two primary contributions. First,
we explore two natural constructions of Legendrian spheres from supporting open book decompositions and show that these always yield the standard Legendrian unknot. Second, in joint work with Hughes, we explore the Legendrians obtained from the doubling
construction in dimension 5, and represent them as Legendrian weaves. We show that a large family of pairwise non-isotopic Legendrians can be obtained by looking at doubles
associated to torus links T(2, n). Further we also mention theorems in progress regarding the fillability of these doubled Legendrians.
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Date Issued
2023-07-17
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Resource Type
Text
Resource Subtype
Dissertation