Splitting numbers of links and the four-genus
HTML articles powered by AMS MathViewer
- by Charles Livingston PDF
- Proc. Amer. Math. Soc. 146 (2018), 421-427 Request permission
Abstract:
The splitting number of a link is the minimum number of crossing changes between distinct components that is required to convert the link into a split link. We provide a bound on the splitting number in terms of the four-genus of related knots.References
- Colin C. Adams, Splitting versus unlinking, J. Knot Theory Ramifications 5 (1996), no. 3, 295–299. MR 1405713, DOI 10.1142/S0218216596000205
- Joshua Batson and Cotton Seed, A link-splitting spectral sequence in Khovanov homology, Duke Math. J. 164 (2015), no. 5, 801–841. MR 3332892, DOI 10.1215/00127094-2881374
- Maciej Borodzik, Stefan Friedl, and Mark Powell, Blanchfield forms and Gordian distance, J. Math. Soc. Japan 68 (2016), no. 3, 1047–1080. MR 3523538, DOI 10.2969/jmsj/06831047
- Maciej Borodzik and Eugene Gorsky, Immersed concordances of links and Heegaard Floer homology, arXiv:1601.07507.
- Jae Choon Cha, Stefan Friedl, and Mark Powell, Splitting numbers of links, arXiv:1308.5638.
- Jae Choon Cha, Charles Livingston, and Daniel Ruberman, Algebraic and Heegaard-Floer invariants of knots with slice Bing doubles, Math. Proc. Cambridge Philos. Soc. 144 (2008), no. 2, 403–410. MR 2405897, DOI 10.1017/S0305004107000795
- David Cimasoni, Slicing Bing doubles, Algebr. Geom. Topol. 6 (2006), 2395–2415. MR 2286030, DOI 10.2140/agt.2006.6.2395
- David Cimasoni, Anthony Conway, and Kleopatra Zacharova, Splitting numbers and signatures, Proc. Amer. Math. Soc. 144 (2016), no. 12, 5443–5455. MR 3556285, DOI 10.1090/proc/13156
- Jennifer Hom, Bordered Heegaard Floer homology and the tau-invariant of cable knots, J. Topol. 7 (2014), no. 2, 287–326. MR 3217622, DOI 10.1112/jtopol/jtt030
- Gahye Jeong, A family of link concordance invariants from perturbed $sl(n)$ homology, arXiv:1608.05781.
- Akio Kawauchi, On links not cobordant to split links, Topology 19 (1980), no. 4, 321–334. MR 584558, DOI 10.1016/0040-9383(80)90017-8
- Peter Kohn, Two-bridge links with unlinking number one, Proc. Amer. Math. Soc. 113 (1991), no. 4, 1135–1147. MR 1079893, DOI 10.1090/S0002-9939-1991-1079893-8
- Peter Ozsváth and Zoltán Szabó, Knot Floer homology and the four-ball genus, Geom. Topol. 7 (2003), 615–639. MR 2026543, DOI 10.2140/gt.2003.7.615
- Ayaka Shimizu, The complete splitting number of a lassoed link, Topology Appl. 159 (2012), no. 4, 959–965. MR 2876702, DOI 10.1016/j.topol.2011.11.028
Additional Information
- Charles Livingston
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- MR Author ID: 193092
- Email: livingst@indiana.edu
- Received by editor(s): December 2, 2016
- Received by editor(s) in revised form: January 31, 2017
- Published electronically: July 20, 2017
- Additional Notes: The author was supported by a Simons Foundation grant and by NSF-DMS-1505586
- Communicated by: David Futer
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 421-427
- MSC (2010): Primary 57M25
- DOI: https://doi.org/10.1090/proc/13703
- MathSciNet review: 3723151