Connected sums of unstabilized Heegaard splittings are unstabilized

DOI10.2140/gt.2008.12.2327zbMath1152.57020arXivmath/0404058OpenAlexW3101896953MaRDI QIDQ945640

David Bachman

Publication date: 17 September 2008

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0404058

zbMATH Keywords

weak reductiongeneralized Heegaard splittingGordon's conjecture

Mathematics Subject Classification ID

Related Items

A note on the planar surface sum of Heegaard splittings ⋮ A note on the uniqueness of unstabilized Heegaard splittings of amalgamated 3-manifolds ⋮ Unstabilized and uncritical dual Heegaard splitting of product \(I\)-bundle ⋮ RECTANGLE CONDITION FOR COMPRESSION BODIES AND 2-FOLD BRANCHED COVERINGS ⋮ A note on bicompressible surface and unstabilized amalgamated Heegaard splitting ⋮ Heegaard structure respects complicated JSJ decompositions ⋮ CRITICAL HEEGAARD SURFACES OBTAINED BY SELF-AMALGAMATION ⋮ Generalized Heegaard splittings and the disk complex ⋮ On keen weakly reducible Heegaard splittings ⋮ Bilateral self-amalgamation of a Heegaard splitting and Hempel distance ⋮ Stabilizing and destabilizing Heegaard splittings of sufficiently complicated 3-manifolds ⋮ Minimal Heegaard genus of amalgamated 3-manifolds ⋮ Unperturbed weakly reducible non-minimal bridge positions ⋮ Minimal partitions for critical Heegaard splittings ⋮ On unstabilized Heegaard splittings of amalgamated 3-manifolds ⋮ On unstabilized genus three critical Heegaard surfaces ⋮ The amalgamation of high distance Heegaard splittings is always efficient ⋮ A sufficient condition for a self-amalgamation of a Heegaard splitting to be unstabilized ⋮ Topologically minimal surfaces versus self-amalgamated Heegaard surfaces ⋮ Critical bridge spheres for links with arbitrarily many bridges ⋮ A topologically minimal canonical Heegaard splitting of a surface bundle is critical ⋮ Topological index theory for surfaces in 3-manifolds ⋮ Unstabilized and uncritical self-amalgamation along essential subsurfaces ⋮ Unnamed Item ⋮ A note on Heegaard splittings of amalgamated 3-manifolds ⋮ A proof of the Gordon conjecture ⋮ Destabilizing Heegaard splittings of knot exteriors ⋮ Strongly irreducible self-amalgamation of a handlebody ⋮ Some results on Heegaard splitting ⋮ On topologically minimal surfaces of high genus ⋮ ON CRITICAL HEEGAARD SPLITTINGS OF TUNNEL NUMBER TWO COMPOSITE KNOT EXTERIORS

Cites Work

• Reducing Heegaard splittings
• Foliations and the topology of 3-manifolds. III
• Irreducible Heegaard splittings of Seifert fibered spaces are either vertical or horizontal
• Geometry of the complex of curves. II: Hierarchical structure
• Comparing Heegaard splittings of non-Haken 3-manifolds
• Heegaard-Zerlegungen der 3-Sphäre
• Sur les difféomorphismes de la sphère de dimension trois \(\Gamma_ 4 = 0\)
• Nicht-homöomorphe Heegaard-Zerlegungen vom Geschlecht 2 der zusammenhängenden Summe zweier Linsenräume
• The stabilization problem for Heegaard splittings of Seifert fibered spaces
• Critical Heegaard surfaces
• Scindements de Heegaard des espaces lenticulaires
• The Classification of Heegaard Splittings for (Compact Orient Able Surface) × S¹
• Generating tuples of free products
• Unnamed Item
• Unnamed Item
• Unnamed Item