TY - JOUR
T1 - Positive open book decompositions of Stein fillable 3-manifolds along prescribed links
AU - Ishikawa, Masaharu
N1 - Funding Information:
This work is supported by the Sumitomo Foundation, Grant for Basic Japanese Research Project. It is also supported by MEXT, Grant-in-Aid for Young Scientists (B) (No. 16740031).
PY - 2006/3
Y1 - 2006/3
N2 - It is known by Loi and Piergallini that a closed, oriented, smooth 3-manifold is Stein fillable if and only if it has a positive open book decomposition. In the present paper we will show that for every link L in a Stein fillable 3-manifold there exists an additional knot L′ to L such that the link L ∪ L′ is the binding of a positive open book decomposition of the Stein fillable 3-manifold. To prove the assertion, we will use the divide, which is a generalization of real morsification theory of complex plane curve singularities, and 2-handle attachings along Legendrian curves.
AB - It is known by Loi and Piergallini that a closed, oriented, smooth 3-manifold is Stein fillable if and only if it has a positive open book decomposition. In the present paper we will show that for every link L in a Stein fillable 3-manifold there exists an additional knot L′ to L such that the link L ∪ L′ is the binding of a positive open book decomposition of the Stein fillable 3-manifold. To prove the assertion, we will use the divide, which is a generalization of real morsification theory of complex plane curve singularities, and 2-handle attachings along Legendrian curves.
KW - Divide
KW - Lefschetz fibration
KW - Positive open book decomposition
KW - Stein fillable 3-manifold
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U2 - 10.1016/j.top.2005.07.002
DO - 10.1016/j.top.2005.07.002
M3 - Article
AN - SCOPUS:28944435495
SN - 0040-9383
VL - 45
SP - 325
EP - 342
JO - Topology
JF - Topology
IS - 2
ER -