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The Thurston norm and $ 2$-handle addition

Author: Martin Scharlemann
Journal: Proc. Amer. Math. Soc. 100 (1987), 362-366
MSC: Primary 57N10; Secondary 57M35
MathSciNet review: 884480
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Abstract: Suppose a $ 2$-handle is attached to a compact orientable $ 3$-manifold $ M$ along an annulus $ A$ contained in a subsurface $ N$ of $ \partial M$. If $ N$ is compressible in $ M$, but $ N - A$ is not, then the Thurston norm is unaffected. This generalizes a series of results due to Przytycki, Jaco, and Johannson.

References [Enhancements On Off] (What's this?)

  • [J] W. Jaco, Adding a $ 2$-handle to a $ 3$-manifold: an application to property $ R$, Proc. Amer. Math. Soc. 92 (1984), 288-292. MR 754723 (86b:57006)
  • [Joh] K. Johannson, On surfaces in one-relator $ 3$-manifolds, preprint.
  • [P] J. Przytycki, Incompressible surfaces in $ 3$-manifolds, Thesis, Columbia Univ., 1981.
  • [Sc] M. Scharlemann, Outermost forks and a theorem of Jaco, Contemp. Math., vol. 44, Amer. Math. Soc., Providence, R.I., 1985, pp. 189-193. MR 813113 (87e:57021)
  • [Th] W. Thurston, A norm for the homology of $ 3$-manifolds, preprint.

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Article copyright: © Copyright 1987 American Mathematical Society

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