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2017 Detection of knots and a cabling formula for $A$–polynomials
Yi Ni, Xingru Zhang
Algebr. Geom. Topol. 17(1): 65-109 (2017). DOI: 10.2140/agt.2017.17.65

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.

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Yi Ni. Xingru Zhang. "Detection of knots and a cabling formula for $A$–polynomials." Algebr. Geom. Topol. 17 (1) 65 - 109, 2017. https://doi.org/10.2140/agt.2017.17.65

Information

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

zbMATH: 1361.57014
MathSciNet: MR3604373
Digital Object Identifier: 10.2140/agt.2017.17.65

Subjects:
Primary: 57M25

Rights: Copyright © 2017 Mathematical Sciences Publishers

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