Locally unknotted spines of Heegaard splittings (Q813177)

The main result of this paper is the following: If \((\Sigma, H_1, H_2)\) is a strongly irreducible Heegaard splitting for a manifold \(M\) then every spine of \(\Sigma\) is locally unknotted. Thus the spines of the handlebodies of a strongly irreducible Heegaard splitting will intersect a closed ball in a graph which is isotopic into the boundary of the ball.