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Full signature invariants for $L_0(F(t))$


Author: Stefan Friedl
Journal: Proc. Amer. Math. Soc. 133 (2005), 647-653
MSC (2000): Primary 18F25; Secondary 57M27
DOI: https://doi.org/10.1090/S0002-9939-04-07540-9
Published electronically: October 7, 2004
MathSciNet review: 2113910
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $F/\mathbb{Q} $ be a number field closed under complex conjugation. Denote by ${L}_0(F(t))$ the Witt group of hermitian forms over $F(t)$. We find full invariants for detecting non-zero elements in ${L}_0(F(t))\otimes \mathbb{Q} $. This group plays an important role in topology in the work done by Casson and Gordon.


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

  • [CG86] A. Casson, C. Gordon, Cobordism of classical knots, Progr. Math., 62, À la recherche de la topologie perdue, 181-199, Birkhäuser Boston, Boston, MA (1986). MR 0900252
  • [CF64] P. E. Conner, E. E. Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Band 33, Springer-Verlag (1964). MR 0176478 (31:750)
  • [F03] S. Friedl, Eta invariants as sliceness obstructions and their relation to Casson-Gordon invariants, Preprint (2003)
  • [K65] M. Kervaire, On higher dimensional knots, 1965 Differential and Combinatorial Topology, Princeton Univ. Press, Princeton, N.J.: pp. 105-119 (1965). MR 0178475 (31:2732)
  • [L93] S. Lang, Algebra, third edition, Addison-Wesley (1993). MR 0197234 (33:5416)
  • [L69] J. Levine, Knot cobordism groups in codimension two, Commentarii Mathematici Helvetici 44: 229-244 (1969). MR 0246314 (39:7618)
  • [L84] R. Litherland, Cobordism of satellite knots, Contemp. Math. 35, Amer. Math. Soc., Providence, RI: 327-362 (1984). MR 0780587 (86k:57003)
  • [R98] A. Ranicki, High-dimensional knot theory, Springer Monographs in Mathematics, Springer-Verlag, New York (1998). MR 1713074 (2000i:57044)

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Additional Information

Stefan Friedl
Affiliation: Department of Mathematics, Ludwigs-Maximilian University, Theresienstrasse 39, 80333 München, Germany
Address at time of publication: Department of Mathematics, Rice University, 6100 Main Street, Houston, Texas 77005
Email: friedl@mathematik.uni-muenchen.de, friedl@rice.edu

DOI: https://doi.org/10.1090/S0002-9939-04-07540-9
Keywords: $L$--groups, knot theory.
Received by editor(s): June 3, 2003
Received by editor(s) in revised form: October 9, 2003
Published electronically: October 7, 2004
Communicated by: Lance W. Small
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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