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Augmentations and Exact Lagrangian C...

Pan, Yu.

Augmentations and Exact Lagrangian Cobordisms.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Augmentations and Exact Lagrangian Cobordisms./
Author:	Pan, Yu.
Description:	1 online resource (124 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-09(E), Section: B.
Contained By:	Dissertation Abstracts International78-09B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369719611

Augmentations and Exact Lagrangian Cobordisms.
Pan, Yu.

Augmentations and Exact Lagrangian Cobordisms. - 1 online resource (124 pages)

Source: Dissertation Abstracts International, Volume: 78-09(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

To a Legendrian knot, one can associate an Ainfinity 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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369719611Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Augmentations and Exact Lagrangian Cobordisms.
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020 $a 9781369719611
035 $a (MiAaPQ)AAI10257951
035 $a (MiAaPQ)duke:13846
035 $a AAI10257951
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Pan, Yu. $3 1180608
245 1 0 $a Augmentations and Exact Lagrangian Cobordisms.
264 0 $c 2017
300 $a 1 online resource (124 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-09(E), Section: B.
500 $a Adviser: Lenhard Ng.
502 $a Thesis (Ph.D.) $c Duke University $d 2017.
504 $a Includes bibliographical references
520 $a To a Legendrian knot, one can associate an Ainfinity 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.
520 $a 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 Kalman 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 Z2[H1( L)] and distinguish the resulting augmentations.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Duke University. $b Mathematics. $3 1180607
773 0 $t Dissertation Abstracts International $g 78-09B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10257951 $z click for full text (PQDT)

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