Isotoping Heegaard surfaces in neat positions with respect to critical distance Heegaard surfaces |
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Authors: | Ayako Ido |
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Affiliation: | Department of Mathematics, Nara Women?s University, Kitauoyanishi-machi, Nara 630-8506, Japan |
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Abstract: | Suppose a closed orientable 3-manifold M has a genus g Heegaard surface P with distance d(P)=2g. Let Q be another genus g Heegaard surface which is strongly irreducible. Then we show that there is a height function f:M→I induced from P such that by isotopy, Q is deformed into a position satisfying the following; (1) fQ| has 2g+2 critical points p0,p1,…,p2g+1 with f(p0)<f(p1)<f(p2g+1) where p0 is a minimum and p2g+1 is a maximum, and p1,…,p2g are saddles, (2) if we take regular values ri (i=1,…,2g+1) such that f(pi−1)<ri<f(pi), then f−1(ri)∩Q consists of a circle if i is odd, and f−1(ri)∩Q consists of two circles if i is even. |
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Keywords: | 57M27 |
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