A formula for Casson’s invariant
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- by Jim Hoste PDF
- Trans. Amer. Math. Soc. 297 (1986), 547-562 Request permission
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
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A. Casson, Lectures given at M.S.R.I., Berkeley, Calif., 1984-85.
- F. González-Acuña, Dehn’s construction on knots, Bol. Soc. Mat. Mexicana (2) 15 (1970), 58–79. MR 356022
- Richard Hartley, The Conway potential function for links, Comment. Math. Helv. 58 (1983), no. 3, 365–378. MR 727708, DOI 10.1007/BF02564642
- Jim Hoste, The Arf invariant of a totally proper link, Topology Appl. 18 (1984), no. 2-3, 163–177. MR 769289, DOI 10.1016/0166-8641(84)90008-7
- Jim Hoste, The first coefficient of the Conway polynomial, Proc. Amer. Math. Soc. 95 (1985), no. 2, 299–302. MR 801342, DOI 10.1090/S0002-9939-1985-0801342-X
- Louis H. Kauffman, The Conway polynomial, Topology 20 (1981), no. 1, 101–108. MR 592573, DOI 10.1016/0040-9383(81)90017-3
- Hitoshi Murakami, The Arf invariant and the Conway polynomial of a link, Math. Sem. Notes Kobe Univ. 11 (1983), no. 2, 335–344. MR 769040
- Dale Rolfsen, Rational surgery calculus: extension of Kirby’s theorem, Pacific J. Math. 110 (1984), no. 2, 377–386. MR 726496, DOI 10.2140/pjm.1984.110.377
Additional Information
- © Copyright 1986 American Mathematical Society
- 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