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- W2960020933 abstract "We lay the foundations of convex hypersurface theory (CHT) in contact topology, extending the work of Giroux in dimension three. Specifically, we prove that any closed hypersurface in a contact manifold can be $C^0$-approximated by a convex one. We also prove that a $C^0$-generic family of mutually disjoint closed hypersurfaces parametrized by $t in [0,1]$ is convex except at finitely many times $t_1, dots, t_N$, and that crossing each $t_i$ corresponds to a bypass attachment. As applications of CHT, we prove the existence of compatible (relative) open book decompositions for contact manifolds and an existence h-principle for codimension 2 contact submanifolds." @default.
- W2960020933 created "2019-07-23" @default.
- W2960020933 creator A5024904131 @default.
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- W2960020933 date "2019-07-13" @default.
- W2960020933 modified "2023-09-25" @default.
- W2960020933 title "Convex hypersurface theory in contact topology" @default.
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- W2960020933 doi "https://doi.org/10.48550/arxiv.1907.06025" @default.
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