A sufficient condition for the genus of an amalgamated 3-manifold not to go down

Let [Formula: see text] [Formula: see text] be a Heegaard splitting of compact orientable [Formula: see text]-manifold, and [Formula: see text] be an amalgamation along an essential surface [Formula: see text]. In this paper, we show that if there is an essential disk [Formula: see text] in [Formula: see text], such that [Formula: see text] cuts [Formula: see text] into two product [Formula: see text]-bundles, one of which is [Formula: see text], and [Formula: see text] [Formula: see text], then [Formula: see text] is unstabilized and [Formula: see text] is uncritical. We also give a sufficient condition for [Formula: see text] to be critical.

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A sufficient condition for the genus of an amalgamated 3-manifold not to go down

Abstract: In the present paper, we give a sufficient condition for the genus of an amalgamated 3-manifold not to go down as follows: Suppose that there is no essential surface with boundary (

Cited by 3 publications

References 13 publications

Common stabilizations of amalgamated Heegaard splitting and dual Heegaard splitting

Common stabilizations of amalgamated Heegaard splitting and dual Heegaard splitting

A note on bicompressible surface and unstabilized amalgamated Heegaard splitting

On unstabilized Heegaard splittings of amalgamated 3-manifolds

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