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Sl(2,C) Floer Homology for Knots and Knot Surgeries.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Sl(2,C) Floer Homology for Knots and Knot Surgeries./
作者:	Neithalath, Ikshu.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	93 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-03, Section: B.
Contained By:	Dissertations Abstracts International83-03B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28490971
ISBN:	9798538115808

Sl(2,C) Floer Homology for Knots and Knot Surgeries.
Neithalath, Ikshu.

Sl(2,C) Floer Homology for Knots and Knot Surgeries. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 93 p.

Source: Dissertations Abstracts International, Volume: 83-03, Section: B.

Thesis (Ph.D.)--University of California, Los Angeles, 2021.

This item must not be sold to any third party vendors.

We investigate the sheaf-theoretic SL(2,C) Floer cohomology for knots and 3-manifolds presented as surgeries on knots in S3. We establish a relationship between the 3-manifold invariants, HP(Y) and HP#(Y) for Y a surgery on a small knot in S3, and the SL(2,C) Casson invariant defined by Curtis. We use this to compute HP for surgeries on the trefoil and the figure-eight knots. We also compute HP for surgeries on two non-small knots, the granny and square knots. For the knot invariant, we prove that the (τ-weighted, sheaf-theoretic) SL(2,C) Casson-Lin invariant is generically independent of the parameter τ and additive under connected sums of knots in integral homology 3-spheres. This addresses two questions posed by Cote-Manolescu.

ISBN: 9798538115808Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Geometry

Sl(2,C) Floer Homology for Knots and Knot Surgeries.
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300 $a 93 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-03, Section: B.
500 $a Advisor: Manolescu, Ciprian.
502 $a Thesis (Ph.D.)--University of California, Los Angeles, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a We investigate the sheaf-theoretic SL(2,C) Floer cohomology for knots and 3-manifolds presented as surgeries on knots in S3. We establish a relationship between the 3-manifold invariants, HP(Y) and HP#(Y) for Y a surgery on a small knot in S3, and the SL(2,C) Casson invariant defined by Curtis. We use this to compute HP for surgeries on the trefoil and the figure-eight knots. We also compute HP for surgeries on two non-small knots, the granny and square knots. For the knot invariant, we prove that the (τ-weighted, sheaf-theoretic) SL(2,C) Casson-Lin invariant is generically independent of the parameter τ and additive under connected sums of knots in integral homology 3-spheres. This addresses two questions posed by Cote-Manolescu.
590 $a School code: 0031.
650 4 $a Mathematics. $3 515831
650 4 $a Surgery. $3 707153
650 4 $a Applied mathematics. $3 2122814
653 $a Geometry
653 $a Knot
653 $a Manifold
653 $a Topology
690 $a 0405
690 $a 0576
690 $a 0364
710 2 $a University of California, Los Angeles. $b Mathematics 0540. $3 2096468
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793 $a English
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