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| A Note on Heegaard Genus of Self-amalgamated3-Manifold |
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Citation： |
Qilong GUO,Ruifeng QIU,Yanqing ZOU.A Note on Heegaard Genus of Self-amalgamated3-Manifold[J].Chinese Annals of Mathematics B,2015,36(1):51~56 |
| Page view： 1695
Net amount： 1359 |
Authors： |
Qilong GUO; Ruifeng QIU; Yanqing ZOU; |
Foundation： |
supported by the National Natural Science Foundation of China
(No. 11271058). The second author is supported by the National Natural Science Foundation of China
(No. 11171108). |
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| Abstract： |
Let M be a connected orientable compact irreducible 3-manifold. Suppose
that ?M consists of two homeomorphic surfaces F1 and F2, and both F1 and F2 are
compressible in M. Suppose furthermore that g(M,F1) = g(M) + g(F1), where g(M,F1)
is the Heegaard genus of M relative to F1. Let Mf be the closed orientable 3-manifold
obtained by identifying F1 and F2 using a homeomorphism f : F1 → F2. The authors
show that if f is sufficiently complicated, then g(Mf) = g(M,?M) + 1. |
Keywords： |
Heegaard splitting, Self-amalgamated, Sufficiently complicated |
Classification： |
57M27 |
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