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On the third Ohtsuki invariant for the Brieskorn–Hamm manifolds

General Education Division, National Institute of Technology, Oshima College, Komatsu 1091-1, Suooshima-cho, Oshima-gun, Yamaguchi 742-2193, Japan

E-mail Address: tsutsumi@oshima-k.ac.jp

E-mail Address: y-tsutsumi@ecip.kobe-shinwa.ac.jp

Present address: Department of Childhood Education, Faculty of Human Development and Education, Kobe Shinwa Women’s University, 7-13-1 Suzurandai Kitamachi, Kobe 651-1111, Japan.

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https://doi.org/10.1142/S0218216521500346Cited by:0 (Source: Crossref)

Abstract

We calculate the Ohtsuki invariants $λ_{i} (M)$ $(i = 0, 1, 2, 3)$ of every Brieskorn–Hamm manifold $M$ which is a rational homology $3$ -sphere. We denote the order of $H_{1} (M; ℤ)$ by $H$ . By the result, we show that the third Ohtsuki invariant $λ_{3} (M)$ of the Brieskorn–Hamm manifolds $M$ with $H = 1$ is negative, and the third Ohtsuki invariant $λ_{3} (M)$ of most Brieskorn–Hamm manifolds $M$ with $H \geq 2$ is positive.

Keywords:

AMSC: 57M12, 57M27

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