Skip to main content
×
Home
    • Aa
    • Aa

Algebraic and Heegaard–Floer invariants of knots with slice Bing doubles

  • JAE CHOON CHA (a1), CHARLES LIVINGSTON (a2) and DANIEL RUBERMAN (a3)
Abstract
Abstract

If the Bing double of a knot K is slice, then K is algebraically slice. In addition the Heegaard–Floer concordance invariants τ, developed by Ozsváth–Szabó, and δ, developed by Manolescu and Owens, vanish on K.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[4] J. C. Cha and K. H. Ko . Signature invariants of covering links. Trans. Amer. Math. Soc. 358 (2006), 33993412.

[5] T. Cochran and K. Orr . Not all links are concordant to boundary links. Ann. of Math. (2) 138 (1993), 519554.

[6] D. Cimasoni Slicing Bing doubles. Alg. Geom. Topol. 6 (2006) 23952415, msp.warwick.ac.uk/agt/2006/06/p083.xhtml.

[7] K. Habiro Claspers and finite type invariants of links. Geom. Topol. 4 (2000), 183.

[10] A. Kawauchi On links not cobordant to split links. Topology 19 (1980), 321334.

[11] C. Kearton The Milnor signatures of compound knots. Proc. Amer. Math. Soc. 76 (1979), 157160.

[12] V. Krushkal Exponential separation in 4-manifolds. Geom. Topol. 4 (2000), 397405.

[13] V. Krushkal On the relative slice problem and four-dimensional topological surgery. Math. Ann. 315 (1999), 363396.

[15] V. Krushkal and P. Teichner . Alexander duality, gropes and link homotopy. Geom. Topol. 1 (1997), 5169.

[16] J. Levine Knot cobordism groups in codimension two. Comment. Math. Helv. 44 (1969) 229244.

[17] J. Levine Invariants of knot cobordism. Invent. Math. 8 (1969), 98110.

[18] C. Livingston Computations of the Ozsváth–Szabó knot concordance invariant. Geom. Topol. 8 (2004), 735742.

[21] P. Ozsváth and Z. Szabó . Knot Floer homology and the four-ball genus. Geom. Topol. 7 (2003), 615639.

[24] H. Seifert On the homology invariants of knots. Quart. J. Math. Oxford Ser. (2) 1 (1950), 2332.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 7 *
Loading metrics...

Abstract views

Total abstract views: 36 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd May 2017. This data will be updated every 24 hours.