Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on the concordance invariants epsilon and upsilon


Author: Jennifer Hom
Journal: Proc. Amer. Math. Soc. 144 (2016), 897-902
MSC (2010): Primary 57M25, 57N70, 57R58
DOI: https://doi.org/10.1090/proc/12706
Published electronically: May 28, 2015
MathSciNet review: 3430863
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Ozsváth-Stipsicz-Szabó recently defined a one-parameter family $ \Upsilon _K(t)$ of concordance invariants associated to the knot Floer complex. We compare their invariant to the $ \{ -1, 0, 1\}$-valued concordance invariant $ \varepsilon (K)$, which is also associated to the knot Floer complex. In particular, we give an example of a knot $ K$ with $ \Upsilon _K(t) \equiv 0$ but $ \varepsilon (K) \neq 0$.


References [Enhancements On Off] (What's this?)

  • [Hed09] Matthew Hedden, On knot Floer homology and cabling. II, Int. Math. Res. Not. IMRN 12 (2009), 2248-2274. MR 2511910 (2011f:57015)
  • [HHN13] Stephen Hancock, Jennifer Hom, and Michael Newman, On the knot Floer filtration of the concordance group, J. Knot Theory Ramifications 22 (2013), no. 14, 1350084, 30. MR 3190122, https://doi.org/10.1142/S0218216513500843
  • [Hom11a] Jennifer Hom, The knot Floer complex and the smooth concordance group, Comment. Math. Helv. 89 (2014), no. 3, 537-570. MR 3260841, https://doi.org/10.4171/CMH/326
  • [Hom11b] Jennifer Hom, A note on cabling and $ L$-space surgeries, Algebr. Geom. Topol. 11 (2011), no. 1, 219-223. MR 2764041 (2012i:57020), https://doi.org/10.2140/agt.2011.11.219
  • [Hom12] Jennifer Hom, On the concordance genus of topologically slice knots, preprint (2012), to appear in Int. Math. Res. Not. IMRN, available at arXiv:1203.4594v1.
  • [Hom13] Jennifer Hom, An infinite rank summand of topologically slice knots, preprint (2013), to appear in Geom. Topol., available at arXiv:1310.4476v1.
  • [Hom14] Jennifer Hom, Bordered Heegaard Floer homology and the tau-invariant of cable knots, J. Topol. 7 (2014), no. 2, 287-326. MR 3217622, https://doi.org/10.1112/jtopol/jtt030
  • [HW14] Matthew Hedden and Liam Watson, On the geography and botany of knot Floer homology, preprint (2014), arXiv:1404.6913v2.
  • [OS03] Peter Ozsváth and Zoltán Szabó, Knot Floer homology and the four-ball genus, Geom. Topol. 7 (2003), 615-639. MR 2026543 (2004i:57036), https://doi.org/10.2140/gt.2003.7.615
  • [OS04] Peter Ozsváth and Zoltán Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004), no. 1, 58-116. MR 2065507 (2005e:57044), https://doi.org/10.1016/j.aim.2003.05.001
  • [OS05] Peter Ozsváth and Zoltán Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005), no. 6, 1281-1300. MR 2168576 (2006f:57034), https://doi.org/10.1016/j.top.2005.05.001
  • [OSS14] Peter Ozsváth, András Stipsicz, and Zoltán Szabó, Concordance homomorphisms from knot Floer homology, preprint (2014), arXiv:1407.1795.
  • [Ras03] Jacob Andrew Rasmussen, Floer homology and knot complements, ProQuest LLC, Ann Arbor, MI, 2003. Thesis (Ph.D.)-Harvard University. MR 2704683

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 57M25, 57N70, 57R58

Retrieve articles in all journals with MSC (2010): 57M25, 57N70, 57R58


Additional Information

Jennifer Hom
Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
Email: hom@math.columbia.edu

DOI: https://doi.org/10.1090/proc/12706
Received by editor(s): September 28, 2014
Received by editor(s) in revised form: December 29, 2014
Published electronically: May 28, 2015
Additional Notes: The author was partially supported by NSF grant DMS-1307879.
Communicated by: Martin Scharlemann
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society