Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T13:43:01.476Z Has data issue: false hasContentIssue false
  • English
  • Français

Ozsváth Szabó's correction term and lens surgery

Published online by Cambridge University Press:  01 January 2009

MOTOO TANGE
MOTOO TANGE*
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8224, Japan. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We will give an explicit formula of Ozsváth–Szabó's correction terms of lens spaces. Applying the formula to a restriction studied by P. Ozsváth and Z. Szabó in [12] and [13], we obtain several constraints of lens spaces which are constructed by a positive Dehn surgery in 3-sphere. Some of the constraints are results which are analogous to results which were known in [6] and [20] before. The constraints completely determine knots yielding L(p, 1) by positive Dehn surgery.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 1 , January 2009 , pp. 119 - 134
Copyright
Copyright © Cambridge Philosophical Society 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Barkan, P.Sur les sommes de Dedekind et les fractions continues finies. C. R. Acad. Sci. Paris Sér. A-B 284 (1977), A923–A926.Google Scholar
[2]Berge, J. Some knots with surgeries yielding lens spaces. Unpublished manuscript.Google Scholar
[3]Culler, M., Gordon, C. McA., Luecke, J. and Shalen, P.Dehn surgery on knots. Ann. of Math. 125 (1987), 237–300.Google Scholar
[4]Fintushel, R. and Stern, R. J.Constructing lens spaces by surgery on knots. Math. Z. 175 (1) (1980), 33–57.Google Scholar
[5]Goda, H. and Teragaito, M.Dehn surgeries on knots which yield lens spaces and genera of knots. Math. Proc. Camb. Phil. Soc. 129 (2000). no. 3. 501–515.Google Scholar
[6]Kadokami, T. and Yamada, Y. A deformation of the Alexander polynomials of knots yielding lens spaces. preprint.Google Scholar
[7]Kronheimer, P., Mrowka, T., Ozsváth, P. and Szabó, Z. Monopoles and lens space surgeries. arXiv:math.GT/0310164.Google Scholar
[8]Némethi, A.On the Ozsváth-Szabó invariant of negative definite plumbed 3-manifolds. Geometry and Topology 9 (2005) 911–1042.Google Scholar
[9]Némethi, A. and Nicolaescu, L. I.Seiberg–Witten invariants and surface singularities. Geometry and Topology 6 (2002), 269–328.Google Scholar
[10]Nicolaescu, L. I.The Reidemeiser Torsion of 3-Manifolds de Gruyter Studies in Mathematics 30.Google Scholar
[11]Nicolaescu, L. I.Seiberg–Witten invariants of rational homology 3-spheres. Comm. Contemp. Math. 6 (2004), 833–866.CrossRefGoogle Scholar
[12]Ozsváth, P. and Szabó, Z. On the knot Floer homology and lens space surgeries. arXiv:math.GT/0303017.Google Scholar
[13]Ozsváth, P. and Szabó, Z.Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary. Adv. Math. 173 (2003), no. 2. 179–261.CrossRefGoogle Scholar
[14]Ozsváth, P. and Szabó, Z.Holomorphic disks and topological invariants for closed three-manifolds. Ann. of Math. (2) 159 (2004), no. 3. 1027–1158.CrossRefGoogle Scholar
[15]Ozsváth, P. and Szabó, Z.Holomorphic disks and three-manifold invariants: properties and applications. Ann. of Math. (2) 159 (2004), no. 3. 1159–1245.Google Scholar
[16]Ozsváth, P. and Szabó, Z. Holomorphic triangles and invariants for smooth four-manifolds. math.SG/0110169.Google Scholar
[17]Rademacher, H. and Grosswald, E.Dedekind sums. The Carus Mathematical Monographs 16.Google Scholar
[18]Rasmussen, J.Lens space surgeries and a conjecture of Goda and Teragaito. Geom. & Top. 8 (2004), 1013–1031.Google Scholar
[19]Reidemeister, K.Homotopieringe und Linsenräume. Abh. Math. Sem. Univ. Hamburg. 11 (1935), 102–109.Google Scholar
[20]Saito, T.Dehn surgery and (1,1)-knots in lens spaces, Topology Appl. 154 (2007), no. 7. 1502–1515.Google Scholar