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Search: id:A136293
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| A136293 |
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Linear bound on the genera of Heegaard splittings of closed, orientable 3-manifolds that admit a generalized triangulation with n generalized tetrahedra. |
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| 26, 102, 178, 254, 330, 406, 482, 558, 634, 710, 786, 862, 938, 1014, 1090, 1166, 1242, 1318, 1394, 1470, 1546, 1622, 1698, 1774, 1850, 1926, 2002, 2078, 2154, 2230, 2306, 2382, 2458, 2534, 2610, 2686, 2762, 2838, 2914, 2990, 3066, 3142, 3218, 3294, 3370
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OFFSET
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0,1
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COMMENT
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Let N be a closed, orientable 3-manifold that admits a triangulation with t tetrahedra. Let F be a Heegaard surface for N. S. Schleimer showed that if g(F) >= 2^{2^{16}t^2}, then the Hempel distance of F (denoted by d(F)) is at most two. In this paper we prove the following generalization:
Let M be an orientable 3-manifold that admits a generalized triangulation with t generalized tetrahedra. Let S be a Heegaard surface for M. If g(S) >= 76t+26, then d(S) <= 2.
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LINKS
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Tsuyoshi Kobayashi, Yo'av Rieck, A linear bound on the genera of Heegaard splittings with distances greater than two, March 20, 2008.
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FORMULA
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a(n) = 76*n + 26.
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CROSSREFS
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Adjacent sequences: A136290 A136291 A136292 this_sequence A136294 A136295 A136296
Sequence in context: A010014 A095796 A026915 this_sequence A065013 A031434 A042320
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 20 2008
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