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. https://resolver.caltech.edu/CaltechAUTHORS:20150421-115826798
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Abstract
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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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. | ||||||||||||
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Subject Keywords: | knot Floer homology, A-polynomial, cabling formula, Eudave-Muñoz knots | ||||||||||||
Issue or Number: | 1 | ||||||||||||
Classification Code: | Mathematical Subject Classification 2010: Primary: 57M25 | ||||||||||||
DOI: | 10.2140/agt.2017.17.65 | ||||||||||||
Record Number: | CaltechAUTHORS:20150421-115826798 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20150421-115826798 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 56816 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | George Porter | ||||||||||||
Deposited On: | 23 Apr 2015 15:38 | ||||||||||||
Last Modified: | 10 Nov 2021 21:04 |
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