incompressible surfaces and stabilizations of Heegaard splittings
نویسندگان
چکیده
We describe probably the simplest 3-manifold which contains closed separating incompressible surfaces of arbitrarily large genus. Two applications of this observation are given. (1) For any closed, orientable 3-manifold M and any integer m> 0, a surgery on a link inM of at most 2m+1 components will provide a closed, orientable, irreducible 3-manifold containing m disjoint, non-parallel, separating, incompressible surfaces of arbitrarily high genus. (2) There exists a 3-manifold M containing separating incompressible surfaces Sn of genus g(Sn) arbitrarily large, such that the amalgamation of minimal Heegaard splittings of two resulting 3-manifolds cutting along Sn can be stabilized g(Sn)− 3 times to a minimal Heegaard splitting of M .
منابع مشابه
Stabilization of Heegaard Splittings
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