Geodesic
Foliated open books
Licata, Joan E1 ; Vértesi, Vera2
1 Mathematical Sciences Institute, The Australian National University, Canberra, ACT, Australia
2 Department of Mathematics, University of Vienna, Vienna, Austria
Algebraic and Geometric Topology, Tome 24 (2024) no. 6, pp. 3139-3197

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

This paper introduces a new type of open book decomposition for a contact three-manifold with a specified characteristic foliation ℱξ on its boundary. These foliated open books offer a finer tool for studying contact manifolds with convex boundary than existing models, as the boundary foliation carries more data than the dividing set. In addition to establishing fundamental results about the uniqueness and existence of foliated open books, we carefully examine their relationship with the partial open books introduced by Honda, Kazez, and Matić. Foliated open books have user-friendly cutting and gluing properties, and they arise naturally as submanifolds of classical open books for closed three-manifolds. We define three versions of foliated open books (embedded, Morse, and abstract), and we prove the equivalence of these models as well as a Giroux Correspondence which characterizes the foliated open books associated to a fixed triple (M,ξ,ℱ).

DOI : 10.2140/agt.2024.24.3139
Keywords: contact structure, open book, partial open book, open book foliation, characteristic foliation, gluing

Licata, Joan E 1 ; Vértesi, Vera 2

1 Mathematical Sciences Institute, The Australian National University, Canberra, ACT, Australia
2 Department of Mathematics, University of Vienna, Vienna, Austria 
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Licata, Joan E; Vértesi, Vera. Foliated open books. Algebraic and Geometric Topology, Tome 24 (2024) no. 6, pp. 3139-3197. doi: 10.2140/agt.2024.24.3139

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