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On ohtsuki’s invariants of integral homology 3-spheres

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Abstract

We provide some more explicit formulae to facilitate the computation of Ohtsuki’s rational invariants λ n of integral homology 3-spheres extracted from Reshetikhin-TuraevSU(2) quantum invariants. Several interesting consequences will follow from our computation of λ2. One of them says that λ2 is always an integer divisible by 3. It seems interesting to compare this result with the fact shown by Murakami that λ1 is 6 times the Casson invariant. Other consequences include some general criteria for distinguishing homology 3-spheres obtained from surgery on knots by using the Jones polynomial.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 92521, Riverside, CA, U. S. A.

    Xiaosong Lin

  2. Department of Mathematics, Indiana University, 47405, Bloomington, IN, U. S. A.

    Zhenghan Wang

  3. Department of Mathematics, University of California, 92093, La Jolla, CA, U. S. A.

    Zhenghan Wang

Authors
  1. Xiaosong Lin
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  2. Zhenghan Wang
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The first author is supported in part by NSF and the second author is supported by an NSF Postdoctoral Fellowship.

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Lin, X., Wang, Z. On ohtsuki’s invariants of integral homology 3-spheres. Acta Mathematica Sinica 15, 293–316 (1999). https://doi.org/10.1007/BF02650726

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  • DOI: https://doi.org/10.1007/BF02650726

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