2014/11/03 by Yi Ni, Xingru Zhang · 1 citation
Mathematics · #math.GT #msc:57M25 #msc:57M27
paper · pdf · doi:10.2140/agt.2017.17.65
published as Algebr. Geom. Topol. 17 (2017) 65-109 · 29 pages, 5 figures
arxiv created 2014/11/03 · arxiv updated 2017/02/08
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.