Skip to main content
SpringerLink
Log in

A cut-and-paste method for computing the Seifert volumes

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

Abstract.

We use methods from gauge theory to compute the Seifert volumes of 3-manifolds. As applications, we are able to find the Seifert volumes of several hyperbolic manifolds obtained by surgery on 2-bridge knots.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bargmann, V.: Irreducible unitary representations of the Lorentz group. Ann. of Math. 48, 568–640 (1947)

    MathSciNet  MATH  Google Scholar 

  2. Brooks, R., Goldman, W.: The Godbillon-Vey invariant of a transversely homogeneous foliation. Trans. Amer. Math. Soc. 286, 651–664 (1984)

    Google Scholar 

  3. Brooks, R., Goldman, W.: Volumes in Seifert space. Duke Math. J. 51, 529–545 (1984)

    Google Scholar 

  4. Brittenham, M., Wu, Y.-Q.: The classification of exceptional Dehn surgeries on 2-bridge knots. Commun. Anal. Geom. 9, 97–113 (2001)

    MathSciNet  MATH  Google Scholar 

  5. Chern, S.S., Simons, J.: Characteristic forms and geometric invariants. Ann. of Math. 99, 48–69 (1974)

    MATH  Google Scholar 

  6. Culler, M., Shalen, P.B.: Varieties of group representations and splittings of 3-manifolds. Ann. of Math. 117, 109–146 (1983)

    MathSciNet  MATH  Google Scholar 

  7. Freed, D.S.: Classical Chern-Simons theory I. Adv. Math. 113, 237–303 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  8. Godbillon, C., Vey, J.: Un invariant des feuilletages de codimension 1. C.R. Acad. Sci. Paris Sér. A-B 273, A92–A95 (1971)

  9. Kirk, P.A., Klassen, E.P.: Chern-Simons invariants of 3-manifolds and representation spaces of knot groups. Math. Ann. 287, 343–367 (1990)

    MathSciNet  MATH  Google Scholar 

  10. Kirk, P.A., Klassen, E.P.: Chern-Simons invariants of 3-manifolds decomposed along tori and the circle bundle over the representation space of T 2. Commun. Math. Phys. 153, 521–557 (1993)

    MathSciNet  MATH  Google Scholar 

  11. Riley, R.: Nonabelian representations of 2-bridge knot groups. Quart. J. Math. Oxford Ser. (2) 35, 138, 191–208 (1984)

  12. Ramadas, T.R., Singer, I.M., Weitsman, J.: Some comments on Chern-Simons gauge theory. Commun. Math. Phys. 126, 409–420 (1989)

    MathSciNet  MATH  Google Scholar 

  13. Scott, P.: The geometries of 3-manifolds. Bull. London Math. Soc. 15, 401–487 (1983)

    MathSciNet  MATH  Google Scholar 

  14. Thurston, W.P.: Three-dimensional geometry and topology. Vol. 1, edited by Silvio Levy, Princeton University Press, Princeton, NJ, 1997

Download references

Author information

Author notes

  1. Vu The Khoi

    Present address: Hanoi Institute of Mathematics, Box 631, 10000, Hanoi, Vietnam

Authors and Affiliations

  1. Department of Mathematics, Brandeis University, Waltham, MA, 02454, USA

    Vu The Khoi

Authors
  1. Vu The Khoi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vu The Khoi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khoi, V. A cut-and-paste method for computing the Seifert volumes. Math. Ann. 326, 759–801 (2003). https://doi.org/10.1007/s00208-003-0438-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00208-003-0438-5

Keywords

Search

Navigation