Geodesic
Geometric criteria for overtwistedness
Casals, Roger1 ; Murphy, Emmy2 ; Presas, Francisco3
1 Department of Mathematics, University of California Davis, Shields Avenue, Davis, California 95616
2 Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
3 Instituto de Ciencias Matemáticas CSIC, C. Nicolás Cabrera, 13 28049 Madrid, Spain
Journal of the American Mathematical Society, Tome 32 (2019) no. 2, pp. 563-604

Voir la notice de l'article provenant de la source American Mathematical Society

In this article we establish efficient geometric criteria to decide whether a contact manifold is overtwisted. Starting with the original definition, we first relate overtwisted disks in different dimensions and show that a manifold is overtwisted if and only if the Legendrian unknot admits a loose chart. Then we characterize overtwistedness in terms of the monodromy of open book decompositions and contact surgeries. Finally, we provide several applications of these geometric criteria.
DOI : 10.1090/jams/917

Casals, Roger 1 ; Murphy, Emmy 2 ; Presas, Francisco 3

1 Department of Mathematics, University of California Davis, Shields Avenue, Davis, California 95616
2 Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
3 Instituto de Ciencias Matemáticas CSIC, C. Nicolás Cabrera, 13 28049 Madrid, Spain 
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Casals, Roger; Murphy, Emmy; Presas, Francisco. Geometric criteria for overtwistedness. Journal of the American Mathematical Society, Tome 32 (2019) no. 2, pp. 563-604. doi: 10.1090/jams/917

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