2008/08/05 by Jung Hoon Lee, Lee, Jung Hoon
Mathematics · #57N10 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57N10
paper · pdf · doi:10.48550/arxiv.0808.0547
6 pages, 6 figures
arxiv created 2008/08/05 · openalex publication_date 2008/08/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let two Heegaard splittings V1 ∪ W1 and V2 ∪ W2 of a 3-manifold M be given. We consider the union stabilization M=V ∪ W which is a common stabilization of V1 ∪ W1 and V2 ∪ W2 having the property that V=V1 ∪ V2. We show that any two Heegaard splittings of a 3-manifold have a union stabilization. We also give some examples with numerical bounds on the minimal genus of union stabilization. On the other hand, we give an example of a candidate for which the minimal genus of union stabilization is strictly larger than the usual stable genus -- the minimal genus of common stabilization.