On the stable equivalence of open books in three-manifolds
By Emmanuel Giroux, N. Goodman. 2005
73 citations recorded by the source corpus.
We show that two open books in a given closed, oriented three-manifold admit isotopic stabilizations, where the stabilization is made by successive plumbings with Hopf bands, if and only if their associated plane fields are homologous. Since this condition is automatically fulfilled in an integral homology sphere, the theorem implies a conjecture of J Harer, namely, that any fibered link in the three-sphere can be obtained from the unknot by a sequence of plumbings and deplumbings of Hopf bands. The proof presented here involves contact geometry in an essential way. 57M50, 57R17; 57M25, 57R52
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e4fb41b0826685b9d19320d288a229b4ef2638f2
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Foliations and the Geometry of 3-Manifolds (2007, background): “(Giroux–Goodman [107]) Two open book structures on a closed oriented 3-manifold admit isotopic stabilizations if and only if their associated oriented plane fields are homologous.”