2008/07/31 by Tao Li
Mathematics · #Advanced Operator Algebra Research #Boundary (topology) #Genus #Geometric and Algebraic Topology #Heegaard splitting #Homeomorphism (graph theory) #Mathematical Dynamics and Fractals #Surface (topology) #math.GT #msc:57M25 #msc:57M50 #msc:57N10
paper · pdf · doi:10.2140/gt.2010.14.1871
published as Geom. Topol. 14 (2010) 1871-1919 · 38 pages, 2 figures
arxiv created 2010/06/15 · openalex publication_date 2010/07/21 · arxiv updated 2014/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Let M 1 and M 2 be orientable irreducible 3-manifolds with connected boundary and suppose @M 1 @M 2 . Let M be a closed 3-manifold obtained by gluing M 1 to M 2 along the boundary. We show that if the gluing homeomorphism is sufficiently complicated, then M is not homeomorphic to S 3 and all small-genus Heegaard splittings of M are standard in a certain sense. In particular, g.M / D g.M 1 / C g.M 2 / g.@M i /, where g.M / denotes the Heegaard genus of M . This theorem is also true for certain manifolds with multiple boundary components.