Connected sums of unstabilized Heegaard splittings are unstabilized

By David Bachman. 2004

63 citations recorded by the source corpus.

Let M1 and M2 be closed, orientable 3‐manifolds. Let Hi denote a Heegaard surface in Mi . We prove that if H1#H2 comes from stabilizing a lower genus splitting of M1#M2 then one of H1 or H2 comes from stabilizing a lower genus splitting. This answers a question of C Gordon [9, Problem 3.91]. We also show that every unstabilized Heegaard splitting has a unique expression as the connected sum of Heegaard splittings of prime 3‐manifolds.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/26f8a09ffcec87d5c4e7df88c21d48cb314cb312

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In Geometry and Topology

1. David Bachman
2. Maggy Tomova
3. Msri Postdoctoral Fellow

In Mathematical Physics

1. David Bachman
2. Maggy Tomova
3. Msri Postdoctoral Fellow

Citations in the corpus

• Topological Index Theory for surfaces in 3-manifolds (2009, background): “In the next section we show that thestrongly irreduciblesurfaces of Casson and Gordon [CG87] are precisely those that have topological index 1.”