Feuilleter
no. 5
Relative Trisections of Fiber Bundles over the Circle
Rudy Dissler1
1 Institut de Mathématiques de Marseille (I2M), Centre de Mathématiques et Informatique, 39 rue Joliot-Curie, 13453 Marseille Cedex 13, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 33 (2024) no. 5, pp. 1373-1412.

Nous construisons une trisection pour un fibré sur le cercle, orienté et compact, à partir d’un scindement de Heegaard suturé de la fibre. Nous donnons un algorithme pour construire les diagrammes de trisection relatifs associés, à partir d’un diagramme de Heegaard suturé de la fibre. Enfin, nous recollons nos diagrammes à des diagrammes de trisections relatifs déjà existants, retrouvant ainsi les trisections de fibrés sur le cercle fermés, les trisections de variétés spun, et produisant des trisections pour les livres ouverts de dimension 4.

For an oriented 4-dimensional fiber bundle over S 1 , we build a relative trisection from a sutured Heegaard splitting of the fiber. We provide an algorithm to explicitly construct the associated relative trisection diagram, from a sutured Heegaard diagram of the fiber. As an application, we glue our relative trisection diagrams with existing diagrams to recover trisected closed fiber bundles over S 1 and trisected spun manifolds, and to provide trisections for 4-dimensional open-books.

Reçu le :
Accepté le :
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DOI : 10.5802/afst.1801

Rudy Dissler 1

1 Institut de Mathématiques de Marseille (I2M), Centre de Mathématiques et Informatique, 39 rue Joliot-Curie, 13453 Marseille Cedex 13, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Relative {Trisections} of {Fiber} {Bundles} over the {Circle}},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {1373--1412},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 33},
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Rudy Dissler. Relative Trisections of Fiber Bundles over the Circle. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 33 (2024) no. 5, pp. 1373-1412. doi : 10.5802/afst.1801. https://afst.centre-mersenne.org/articles/10.5802/afst.1801/

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