Communications of the
Korean Mathematical Society CKMS

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.

Keywords: Casson invariant, Dehn surgery, homology $3$-sphere, $\mu$-invariants, net diagram, $4$-manifold

MSC numbers: Primary 57M25, 57M27