2004/04/30 by David Bachman
Mathematics · #Advanced Operator Algebra Research #Genus #Geometric and Algebraic Topology #Heegaard splitting #Link (geometry) #Mathematical Dynamics and Fractals #Prime (order theory) #Surface (topology) #math.GT #msc:57M99
paper · pdf · doi:10.2140/gt.2008.12.2327
published as Geom. Topol. 12 (2008) 2327-2378 · 41 pages, 19 figures. This is a complete revision to remove the assumption that the component manifolds are irreducible, thereby obtaining a proof of Gordon's conjecture with no additional assumptions. Many examples and figures have also been added for improved readability
arxiv created 2006/09/13 · openalex publication_date 2008/09/15 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
be closed, orientable 3-manifolds. Let H i denote a Heegaard surface in M i . We prove that if H 1 #H 2 comes from stabilizing a lower genus splitting of M 1 #M 2 then one of H 1 or H 2 comes from stabilizing a lower genus splitting. This answers a question of C Gordon We also show that every unstabilized Heegaard splitting has a unique expression as the connected sum of Heegaard splittings of prime 3-manifolds.