A note on Heegaard genus of self-amalgamated 3-manifold

Autor: Qilong Guo, Ruifeng Qiu, Yanqing Zou
Rok vydání: 2014
Předmět:
Zdroj: Chinese Annals of Mathematics, Series B. 36:51-56
ISSN: 1860-6261
0252-9599
DOI: 10.1007/s11401-014-0877-1
Popis: 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.
Databáze: OpenAIRE
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