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You searched for subject:( Lengendrian knots). One record found.

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1. Pan, YU. Augmentations and exact Lagrangian cobordisms .

Degree: 2017, Duke University

To a Legendrian knot, one can associate an A category, the augmentation category. An exact Lagrangian cobordism between two Legendrian knots gives a functor of the augmentation categories of the two knots. We study the functor and establish a long exact sequence relating the corresponding cohomology of morphisms of the two ends. As applications, we prove that the functor between augmentation categories is injective on the level of equivalence classes of objects and find new obstructions to the existence of exact Lagrangian cobordisms in terms of linearized contact homology and ruling polynomials. As a related project, we study exact Lagrangian fillings of Legendrian (2,n) links. For a Legendrian (2,n) torus knot or link with maximal Thurston – Bennequin number, Ekholm, Honda, and K{\'a}lm{\'a}n constructed Cn exact Lagrangian fillings, where Cn is the n – th Catalan number. We show that these exact Lagrangian fillings are pairwise non – isotopic through exact Lagrangian isotopy. To do that, we compute the augmentations induced by the exact Lagrangian fillings L to \mathbbZ2[H1(L)] and distinguish the resulting augmentations. Advisors/Committee Members: Ng, Lenhard (advisor).

Subjects/Keywords: Mathematics; Augmentations; Contact Topology; Lagrangian cobordisms; Lengendrian knots

…special knots in contact manifolds, the Legendrian knots. 1 In 2009, Nadler and Zaslow [… …homological mirror symmetry) through sheaf theory. In 2014, Legendrian knots was introduced… …Legendrian knots [STZ]. Analogous to the Nadler–Zaslow correspondence, a correspondence… …plane field ξ everywhere. In geometric topology, given two knots in R3 , an interesting object… …to study is a surface in R3 ˆ r0, 1s connecting the two knots, called a cobordism. There is… 

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APA (6th Edition):

Pan, Y. (2017). Augmentations and exact Lagrangian cobordisms . (Thesis). Duke University. Retrieved from http://hdl.handle.net/10161/14398

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Pan, YU. “Augmentations and exact Lagrangian cobordisms .” 2017. Thesis, Duke University. Accessed March 08, 2021. http://hdl.handle.net/10161/14398.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Pan, YU. “Augmentations and exact Lagrangian cobordisms .” 2017. Web. 08 Mar 2021.

Vancouver:

Pan Y. Augmentations and exact Lagrangian cobordisms . [Internet] [Thesis]. Duke University; 2017. [cited 2021 Mar 08]. Available from: http://hdl.handle.net/10161/14398.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Pan Y. Augmentations and exact Lagrangian cobordisms . [Thesis]. Duke University; 2017. Available from: http://hdl.handle.net/10161/14398

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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