## On surfaces and Heegaard surfaces

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- by Klaus Johannson PDF
- Trans. Amer. Math. Soc.
**325**(1991), 573-591 Request permission

## 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.## References

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## Additional Information

- © Copyright 1991 American Mathematical Society
- 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