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A-Infinity Sabloff Duality via the L...

Chen, Zhenyi,

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A-Infinity Sabloff Duality via the LSFT Algebra /

Record Type:	Electronic resources : Monograph/item
Title/Author:	A-Infinity Sabloff Duality via the LSFT Algebra // Zhenyi Chen.
Author:	Chen, Zhenyi,
Description:	1 electronic resource (122 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
Contained By:	Dissertations Abstracts International86-12B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32001680
ISBN:	9798315799757

A-Infinity Sabloff Duality via the LSFT Algebra /
Chen, Zhenyi,

A-Infinity Sabloff Duality via the LSFT Algebra /Zhenyi Chen. - 1 electronic resource (122 pages)

Source: Dissertations Abstracts International, Volume: 86-12, Section: B.

We use Ng's LSFT algebra to upgrade Sabloff duality of Legendrian knots to a quasi-isomorphism of A∞ bimodules over the positive augmentation category Aug+. We also extend the Ekholm-Etnyre-Sabloff exact sequence to an exact sequence of Aug+-bimodules, using a quotient category C of short Reeb chords. In addition, we define curved augmentations of the LSFT algebra and show that they can be used to construct a homotopy inverse of the A∞ Sabloff map, together with all higher homotopies. The above results suggest a conjectural recipe for an explicit weak relative Calabi-Yau structure on the quotient A∞ functor π : Aug+ → C.

English

ISBN: 9798315799757Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

LSFT algebra

A-Infinity Sabloff Duality via the LSFT Algebra /
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100 1 $a Chen, Zhenyi, $e author. $0 (orcid)0000-0003-1610-9310 $3 3823123
245 1 0 $a A-Infinity Sabloff Duality via the LSFT Algebra / $c Zhenyi Chen.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2025
300 $a 1 electronic resource (122 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
500 $a Advisors: Zaslow, Eric Committee members: Schrader, Gus; Tamarkin, Dmitry.
502 $b Ph.D. $c Northwestern University $d 2025.
520 $a We use Ng's LSFT algebra to upgrade Sabloff duality of Legendrian knots to a quasi-isomorphism of A∞ bimodules over the positive augmentation category Aug+. We also extend the Ekholm-Etnyre-Sabloff exact sequence to an exact sequence of Aug+-bimodules, using a quotient category C of short Reeb chords. In addition, we define curved augmentations of the LSFT algebra and show that they can be used to construct a homotopy inverse of the A∞ Sabloff map, together with all higher homotopies. The above results suggest a conjectural recipe for an explicit weak relative Calabi-Yau structure on the quotient A∞ functor π : Aug+ → C.
546 $a English
590 $a School code: 0163
650 4 $a Mathematics. $3 515831
650 4 $a Applied mathematics. $3 2122814
650 4 $a Computational physics. $3 3343998
653 $a LSFT algebra
653 $a Quasi-isomorphism
653 $a Legendrian knots
653 $a Augmentation category
690 $a 0405
690 $a 0216
690 $a 0364
710 2 $a Northwestern University. $b Mathematics. $e degree granting institution. $3 3823124
720 1 $a Zaslow, Eric $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-12B.
790 $a 0163
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32001680