Geodesic
Detection of knots and a cabling formula for A–polynomials
Ni, Yi1 ; Zhang, Xingru2
1Department of Mathematics, Caltech, 1200 E California Blvd, Pasadena, CA 91125, United States
2Department of Mathematics, University at Buffalo, 111 Mathematics Building, Buffalo, NY 14260-2900, United States
Algebraic and Geometric Topology, Tome 17 (2017) no. 1, pp. 65-109
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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.

DOI : 10.2140/agt.2017.17.65
Classification : 57M25
Keywords: knot Floer homology, A-polynomial, cabling formula, Eudave-Muñoz knots

Ni, Yi  1   ; Zhang, Xingru  2

1 Department of Mathematics, Caltech, 1200 E California Blvd, Pasadena, CA 91125, United States
2 Department of Mathematics, University at Buffalo, 111 Mathematics Building, Buffalo, NY 14260-2900, United States 
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Ni, Yi; Zhang, Xingru. Detection of knots and a cabling formula for A–polynomials. Algebraic and Geometric Topology, Tome 17 (2017) no. 1, pp. 65-109. doi: 10.2140/agt.2017.17.65

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