Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A formula for Casson's invariant


Author: Jim Hoste
Journal: Trans. Amer. Math. Soc. 297 (1986), 547-562
MSC: Primary 57M25; Secondary 57N10
DOI: https://doi.org/10.1090/S0002-9947-1986-0854084-4
MathSciNet review: 854084
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Suppose $ H$ is a homology $ 3$-sphere obtained by Dehn surgery on a link $ L$ in a homology $ 3$-sphere $ M$. If every pair of components of $ L$ has zero linking number in $ M$, then we give a formula for the Casson invariant, $ \lambda (H)$, in terms of $ \lambda (M)$, the surgery coefficients of $ L$, and a certain coefficient from each of the Conway polynomials of $ L$ and all its sublinks. A few consequences of this formula are given.


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

  • [1] A. Casson, Lectures given at M.S.R.I., Berkeley, Calif., 1984-85.
  • [2] F. González-Acuña, Dehn's construction on knots, Bol. Soc. Mat. Mexicana 15 (1970), 58-79. MR 0356022 (50:8495)
  • [3] R. Hartley, The Conway potential function for links, Comment. Math. Helv. 58 (1983), 365-378. MR 727708 (85h:57006)
  • [4] J. Hoste, The Arf invariant of a totally proper link, Topology Appl. 18 (1984), 163-177. MR 769289 (86i:57009)
  • [5] -, The first coefficient of the Conway polynomial, Proc. Amer. Math. Soc. 95 (1985), 299-302. MR 801342 (86m:57009)
  • [6] L. H. Kauffman, The Conway polynomial, Topology 20 (1981), 101-108. MR 592573 (81m:57004)
  • [7] H. Murakami, The Arf invariant and the Conway polynomial of a link, Math. Sem. Notes Kobe Univ. 11 (1983), 335-344. MR 769040 (86g:57006)
  • [8] D. Rolfsen, Rational surgery calculus: Extension of Kirby's theorem, Pacific J. Math. 110 (1984), 377-386. MR 726496 (85h:57009)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57M25, 57N10

Retrieve articles in all journals with MSC: 57M25, 57N10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1986-0854084-4
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society