Scharlemann-Thompson untelescoping of Heegaard splittings is finer than Casson-Gordon's

摘要

We show that there exist infinitely many 3-manifolds M, each of which admits a genus 4 Heegaard splitting V ∪_P W such that there is a Scharlemann-Thompson untelescoping of V ∪_P W which decomposes M into three pieces, and that any Casson-Gordon untelescoping of V ∪_P W decomposed M into exactly two pieces.