The Thurston norm and $2$-handle addition
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- by Martin Scharlemann PDF
- Proc. Amer. Math. Soc. 100 (1987), 362-366 Request permission
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
- William Jaco, Adding a $2$-handle to a $3$-manifold: an application to property $R$, Proc. Amer. Math. Soc. 92 (1984), no. 2, 288–292. MR 754723, DOI 10.1090/S0002-9939-1984-0754723-6 K. Johannson, On surfaces in one-relator $3$-manifolds, preprint. J. Przytycki, Incompressible surfaces in $3$-manifolds, Thesis, Columbia Univ., 1981.
- Martin Scharlemann, Outermost forks and a theorem of Jaco, Combinatorial methods in topology and algebraic geometry (Rochester, N.Y., 1982) Contemp. Math., vol. 44, Amer. Math. Soc., Providence, RI, 1985, pp. 189–193. MR 813113, DOI 10.1090/conm/044/813113 W. Thurston, A norm for the homology of $3$-manifolds, preprint.
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 362-366
- MSC: Primary 57N10; Secondary 57M35
- DOI: https://doi.org/10.1090/S0002-9939-1987-0884480-7
- MathSciNet review: 884480