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Detection of knots and a cabling formula for A-polynomials

Ni, Yi and Zhang, Xingru (2017) Detection of knots and a cabling formula for A-polynomials. Algebraic and Geometric Topology, 17 (1). pp. 65-109. ISSN 1472-2747. doi:10.2140/agt.2017.17.65.

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We say that a given knot J ⊂ S^3 is detected by its knot Floer homology and AA–polynomial if whenever a knot K ⊂ S^3 has the same knot Floer homology and the same A–polynomial as J, then K=J. In this paper we show that every torus knot T(p,q) is detected by its knot Floer homology and A–polynomial. We also give a one-parameter family of infinitely many hyperbolic knots in S^3 each of which is detected by its knot Floer homology and AA–polynomial. In addition we give a cabling formula for the AA–polynomials of cabled knots in S^3, which is of independent interest. In particular we give explicitly the AA–polynomials of iterated torus knots.

Item Type:Article
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URLURL TypeDescription 10.2140/agt.2017.17.65DOIArticle Paper
Additional Information: © 2017 Mathematical Sciences Publishers. Received: 26 March 2015; Revised: 9 May 2016; Accepted: 19 May 2016; Published: 26 January 2017. Ni was partially supported by NSF grant numbers DMS-1103976 and DMS-1252992 and an Alfred P Sloan Research Fellowship.
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:knot Floer homology, A-polynomial, cabling formula, Eudave-Muñoz knots
Issue or Number:1
Classification Code:Mathematical Subject Classification 2010: Primary: 57M25
Record Number:CaltechAUTHORS:20150421-115826798
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56816
Deposited By: George Porter
Deposited On:23 Apr 2015 15:38
Last Modified:10 Nov 2021 21:04

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