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A distribution of rational homology $3$ $3$ -spheres captured by the CWL invariant Phase 1

Noriko Maruyama

Musashino Art University, 1-736 Ogawa-Machi, Kodaira, Tokyo 187-8505, Japan

https://doi.org/10.1142/S0218216517500547Cited by:3 (Source: Crossref)

Abstract

Taking advantage of a numerical invariant, we visualize a distribution of rational homology 3-spheres on a plane via the Casson–Walker–Lescop (CWL) invariant and observe several aspects of the distribution. In particular, we study the characteristics of the distribution of lens spaces as a fundamental family of rational homology 3-spheres with a way to yield a family of estimation for the Dedekind sum. The CWL invariant captures the finiteness of lens space surgeries along knots. According to the finiteness, for example, the CWL invariant determines possible lens spaces as the results of integral surgeries along a knot $K$ $K$ with $a_{1} (K) = 12$ $a_{1} (K) = 12$ .

Keywords:

AMSC: 11F20, 57M27

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