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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On Vassiliev knot invariants induced
from finite type 3-manifold invariants


Authors: Matt Greenwood and Xiao-Song Lin
Journal: Trans. Amer. Math. Soc. 351 (1999), 3659-3672
MSC (1991): Primary 57M25
Published electronically: May 3, 1999
MathSciNet review: 1467465
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the knot invariant induced by a $\mathbb{Z}$-homology 3-sphere invariant of order $\leq k$ in Ohtsuki's sense, where $k\geq 4$, is of order $\leq k-2$. The method developed in our computation shows that there is no $\mathbb{Z}$-homology 3-sphere invariant of order 5.


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Additional Information

Matt Greenwood
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: matt@math.columbia.edu

Xiao-Song Lin
Affiliation: Department of Mathematics, University of California, Riverside, California 92521
Email: xl@math.ucr.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02139-X
PII: S 0002-9947(99)02139-X
Received by editor(s): June 29, 1995
Received by editor(s) in revised form: May 2, 1997
Published electronically: May 3, 1999
Additional Notes: The second author is supported in part by NSF
Article copyright: © Copyright 1999 American Mathematical Society