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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On surfaces and Heegaard surfaces


Author: Klaus Johannson
Journal: Trans. Amer. Math. Soc. 325 (1991), 573-591
MSC: Primary 57N10; Secondary 57N05
DOI: https://doi.org/10.1090/S0002-9947-1991-1064268-2
MathSciNet review: 1064268
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Abstract: This paper is concerned with the intersection of surfaces and Heegaard surfaces in closed orientable $ 3$-manifolds $ M$. Given a Heegaard decomposition $ (M,{V_1},{V_2})$ it will be shown that any surface (orientable or not) in $ M$ is equivalent to a surface which intersects $ {V_1}$ in discs whose total number is limited from above by some function in the genus of $ \partial {V_1}$ alone. The equivalence relation in question is generated by disc- and annulus-compressions.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1064268-2
Article copyright: © Copyright 1991 American Mathematical Society