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About: Open book decomposition     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatTheoremsInGeometryyago:WikicatTheoremsInTopologyyago:Abstraction100002137yago:Communication100033020yago:Message106598915yago:Proposition106750804yago:Statement106722453yago:Theorem106752293 New Facet based on Instances of this Class

In mathematics, an open book decomposition (or simply an open book) is a decomposition of a closed oriented 3-manifold M into a union of surfaces (necessarily with boundary) and solid tori. Open books have relevance to contact geometry, with a famous theorem of Emmanuel Giroux (given below) that shows that contact geometry can be studied from an entirely topological viewpoint.