On 3–braid knots of finite concordance order

Lisca, Paolo

doi:10.1090/tran/6888

On 3–braid knots of finite concordance order
HTML articles powered by AMS MathViewer

by Paolo Lisca PDF

Trans. Amer. Math. Soc. 369 (2017), 5087-5112 Request permission

Abstract:

We study 3–braid knots of finite smooth concordance order. A corollary of our main result is that a chiral 3–braid knot of finite concordance order is ribbon.

References

John A. Baldwin, Heegaard Floer homology and genus one, one-boundary component open books, J. Topol. 1 (2008), no. 4, 963–992. MR 2461862, DOI 10.1112/jtopol/jtn029
Joan S. Birman and William W. Menasco, Studying links via closed braids. III. Classifying links which are closed $3$-braids, Pacific J. Math. 161 (1993), no. 1, 25–113. MR 1237139, DOI 10.2140/pjm.1993.161.25
A. J. Casson and C. McA. Gordon, Cobordism of classical knots, À la recherche de la topologie perdue, Progr. Math., vol. 62, Birkhäuser Boston, Boston, MA, 1986, pp. 181–199. With an appendix by P. M. Gilmer. MR 900252
Jae C. Cha and Charles Livingston, Knotinfo: Table of knot invariants, http://www.indiana.edu/~knotinfo, \today.
Andrew Donald, Embedding Seifert manifolds in $S^4$, Trans. Amer. Math. Soc. 367 (2015), no. 1, 559–595. MR 3271270, DOI 10.1090/S0002-9947-2014-06174-6
S. K. Donaldson, The orientation of Yang-Mills moduli spaces and $4$-manifold topology, J. Differential Geom. 26 (1987), no. 3, 397–428. MR 910015, DOI 10.4310/jdg/1214441485
Dieter Erle, Calculation of the signature of a 3-braid link, Kobe J. Math. 16 (1999), no. 2, 161–175. MR 1745024
C. McA. Gordon and R. A. Litherland, On the signature of a link, Invent. Math. 47 (1978), no. 1, 53–69. MR 500905, DOI 10.1007/BF01609479
Joshua Greene and Stanislav Jabuka, The slice-ribbon conjecture for 3-stranded pretzel knots, Amer. J. Math. 133 (2011), no. 3, 555–580. MR 2808326, DOI 10.1353/ajm.2011.0022
Joshua Evan Greene, Donaldson’s theorem, Heegaard Floer homology, and knots with unknotting number one, Adv. Math. 255 (2014), 672–705. MR 3167496, DOI 10.1016/j.aim.2014.01.018
Shin’ichi Kinoshita and Hidetaka Terasaka, On unions of knots, Osaka Math. J. 9 (1957), 131–153. MR 98386
Ana G. Lecuona, On the slice-ribbon conjecture for Montesinos knots, Trans. Amer. Math. Soc. 364 (2012), no. 1, 233–285. MR 2833583, DOI 10.1090/S0002-9947-2011-05385-7
Ana G. Lecuona, On the slice-ribbon conjecture for pretzel knots, Algebr. Geom. Topol. 15 (2015), no. 4, 2133–2173. MR 3402337, DOI 10.2140/agt.2015.15.2133
Paolo Lisca, Lens spaces, rational balls and the ribbon conjecture, Geom. Topol. 11 (2007), 429–472. MR 2302495, DOI 10.2140/gt.2007.11.429
Paolo Lisca, Sums of lens spaces bounding rational balls, Algebr. Geom. Topol. 7 (2007), 2141–2164. MR 2366190, DOI 10.2140/agt.2007.7.2141
Paolo Lisca, Stein fillable contact 3-manifolds and positive open books of genus one, Algebr. Geom. Topol. 14 (2014), no. 4, 2411–2430. MR 3331617, DOI 10.2140/agt.2014.14.2411
Charles Livingston, A survey of classical knot concordance, Handbook of knot theory, Elsevier B. V., Amsterdam, 2005, pp. 319–347. MR 2179265, DOI 10.1016/B978-044451452-3/50008-3
Ciprian Manolescu and Brendan Owens, A concordance invariant from the Floer homology of double branched covers, Int. Math. Res. Not. IMRN 20 (2007), Art. ID rnm077, 21. MR 2363303, DOI 10.1093/imrn/rnm077
Kunio Murasugi, On closed $3$-braids, Memoirs of the American Mathematical Society, No. 151, American Mathematical Society, Providence, R.I., 1974. MR 0356023
Stepan Yu. Orevkov, Quasipositivity problem for 3-braids, Turkish J. Math. 28 (2004), no. 1, 89–93. MR 2056762
Lee Rudolph, Braided surfaces and Seifert ribbons for closed braids, Comment. Math. Helv. 58 (1983), no. 1, 1–37. MR 699004, DOI 10.1007/BF02564622
Lee Rudolph, Quasipositivity as an obstruction to sliceness, Bull. Amer. Math. Soc. (N.S.) 29 (1993), no. 1, 51–59. MR 1193540, DOI 10.1090/S0273-0979-1993-00397-5