# HOMOLOGY 3-SPHERES OBTAINED BY SURGERY ON EVEN NET DIAGRAMS

• Lee, Sang-Youl (Department of Mathematics Pusan National University)
• Published : 2012.10.31

#### Abstract

In this paper, we characterize surgery presentations for $\mathbb{Z}$-homology 3-spheres and $\mathbb{Z}/2\mathbb{Z}$-homology 3-spheres obtained from $S^3$ by Dehn surgery along a knot or link which admits an even net diagram and show that the Casson invariant for $\mathbb{Z}$-homology spheres and the ${\mu}$-invariant for $\mathbb{Z}/2\mathbb{Z}$-homology spheres can be directly read from the net diagram. We also construct oriented 4-manifolds bounding such homology spheres and find their some properties.

#### Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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