On the existence of infinitely many essential surfaces of bounded genus

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Abstract

A theorem of William Jaco and Eric Sedgwick states that if M is an irreducible, ∂-irreducible 3-manifold with boundary a single torus, and if M contains no genus one essential (incompressible and ∂-incompressible) surfaces, then M cannot contain infinitely many distinct isotopy classes of essential surfaces of uniformly bounded genus. The main result in this paper is a generalization: If M is an irreducible ∂-irreducible 3-manifold with boundary, and M contains no genus one or genus zero essential surfaces, then M cannot contain infinitely many isotopy classes of essential surfaces of uniformly bounded genus.

Original languageEnglish (US)
Pages (from-to)449-458
Number of pages10
JournalPacific Journal of Mathematics
Volume202
Issue number2
DOIs
StatePublished - Jan 1 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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