Algebraic & Geometric Topology

Detection of knots and a cabling formula for $A$–polynomials

Yi Ni and Xingru Zhang

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Abstract

We say that a given knot J S3 is detected by its knot Floer homology and A–polynomial if whenever a knot K S3 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 S3 each of which is detected by its knot Floer homology and A–polynomial. In addition we give a cabling formula for the A–polynomials of cabled knots in S3, which is of independent interest. In particular we give explicitly the A–polynomials of iterated torus knots.

Article information

Source
Algebr. Geom. Topol., Volume 17, Number 1 (2017), 65-109.

Dates
Received: 26 March 2015
Revised: 9 May 2016
Accepted: 19 May 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841309

Digital Object Identifier
doi:10.2140/agt.2017.17.65

Mathematical Reviews number (MathSciNet)
MR3604373

Zentralblatt MATH identifier
1361.57014

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
knot Floer homology A-polynomial cabling formula Eudave-Muñoz knots

Citation

Ni, Yi; Zhang, Xingru. Detection of knots and a cabling formula for $A$–polynomials. Algebr. Geom. Topol. 17 (2017), no. 1, 65--109. doi:10.2140/agt.2017.17.65. https://projecteuclid.org/euclid.agt/1510841309


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