3-dimensional bordism (Q908553)

Generalizing an argument of Rourke, the authors give elementary proofs of theorems of Rokhlin-Thom and Milnor which state that every closed oriented 3-manifold is the boundary of a compact oriented 4-manifold (i.e. \(\Omega_ 3^{O}=0)\) and that every closed spin 3-manifold is the boundary of a compact spin 4-manifold (i.e. \(\Omega_ 3^{Spin}=0)\). The proofs are based on Heegaard diagrams of 3-manifolds and properties of systems of curves on surfaces.