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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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On surfaces and Heegaard surfaces
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by Klaus Johannson PDF
Trans. Amer. Math. Soc. 325 (1991), 573-591 Request permission


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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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 325 (1991), 573-591
  • MSC: Primary 57N10; Secondary 57N05
  • DOI:
  • MathSciNet review: 1064268