A refinement of Johnson's bounding for the stable genera of Heegaard splittings

For each integer k > 1, Johnson gave a 3-manifold with Heegaard splittings of genera 2k and 2k-1 such that any common stabilization of these two surfaces has genus at least 3k-1. We modify his argument to produce a 3-manifold with two Heegaard splitings of genus 2k such that any common stabilization of them has genus at least 3k.Comment: 16 pages, 17 figure

Instanton effects and Witten complex in supersymmetric quantum mechanics on SO(4)

We examine supersymmetric quantum mechanics on $SO(4)$ to realize Witten's idea. We find instanton solutions connecting approximate vacuums. We calculate Hessian matrices for these solutions to determine true vacuums. Our result is in agreement with de Rham cohomology of $SO(4)$. We also give a criterion for cancellation of instanton effects for a pair of instanton paths.Comment: 26pages, Late

Simple procedure for classical signal-procession in cluster-state quantum computation

We exhibit a simple procedure to find how classical signals should be processed in cluster-state quantum computation. Using stabilizers characterizing a cluster state, we can easily find a precise classical signal-flow that is required in performing cluster-state computation.Comment: 5pages, 5figure