Tsuyoshi Kobayashi

Publications (2)1.3 Total impact

• Article: The amalgamation of high distance Heegaard splittings is always efficient

  Tsuyoshi Kobayashi, Ruifeng Qiu
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  ABSTRACT: Let M be a compact orientable manifold, and F be an essential closed surface which cuts M into two 3-manifolds M 1 and M 2. Let Mi=ViÈSi Wi{M_{i}=V_{i}\cup_{S_{i}} W_{i}} be a Heegaard splitting for i=1, 2. We denote by d(S i ) the distance of ViÈSi Wi{V_{i}\cup_{S_{i}} W_{i}} . If d(S 1), d(S 2)≥ 2(g(M 1)+g(M 2)−g(F)), then M has a unique minimal Heegaard splitting up to isotopy, i.e. the amalgamation of V1ÈS1 W1{V_{1}\cup_{S_{1}} W_{1}} and V2ÈS2 W2{V_{2}\cup_{S_{2}} W_{2}} .
  Mathematische Annalen 04/2012; 341(3):707-715. · 1.30 Impact Factor
• Source

  Available from: uark.edu

  Article: Separating incompressible surfaces and stabilizations of Heegaard splittings

  Tsuyoshi Kobayashi, Ruifeng Qiu, Av Rieck, Shicheng Wang Lmam
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  ABSTRACT: We describe probably the simplest 3-manifold which contains closed separating incompressible surfaces of arbitrarily large genus. Two applications of this observa-tion are given. (1) For any closed, orientable 3-manifold M and any integer m > 0, a surgery on a link in M of at most 2m + 1 components will provide a closed, orientable, irreducible 3-manifold containing m disjoint, non-parallel, separating, incompress-ible surfaces of arbitrarily high genus. (2) There exists a 3-manifold M containing separating incompressible surfaces S n of genus g(S n) arbitrarily large, such that the amalgamation of minimal Heegaard splittings of two resulting 3-manifolds cutting along S n can be stabilized g(S n) − 3 times to a minimal Heegaard splitting of M .
  Math. Proc. Camb. Phil. Soc. 01/2004; 137(633).