Note on three-fold branched covers of S 4
[Remarque sur les revêtements de degré 3 de S 4 ]
Blair, Ryan1 ; Cahn, Patricia2 ; Kjuchukova, Alexandra3 ; Meier, Jeffrey4
1 Department of Mathematics and Statistics 1250 Bellflower Boulevard Long Beach, California 90840 (USA)
2 Department of Mathematics & Statistics Clark Science Center Smith College Burton Hall 115 Northampton, MA 01063 (USA)
3 Department of Mathematics University of Notre Dame 255 Hurley Bldg Notre Dame, IN 46556 (USA)
4 Department of Mathematics Western Washington University 516 High Street, Bellingham, WA 98229 (USA)
Annales de l'Institut Fourier, Online first, 18 p.

Nous montrons que toute variété de dimension 4 admettant une (g;k 1 ,k 2 ,0)-trisection est un revêtement irrégulier de degré 3 de la 4-sphère dont l’ensemble de ramification est une surface dans S 4 , plongée de manière lisse à l’exception d’un point singulier qui est un cône sur un entrelacs. Une 4-variété admet une telle trisection si et seulement si elle a une décomposition en anses sans 1-anses ; il est conjecturé que toutes les variétés de dimension 4 simplement connexes ont cette propriété.

We show that any 4-manifold admitting a (g;k 1 ,k 2 ,0)-trisection is an irregular 3-fold cover of the 4-sphere whose branching set is a surface in S 4 , smoothly embedded except for one singular point which is the cone on a link. A 4-manifold admits such a trisection if and only if it has a handle decomposition with no 1-handles; it is conjectured that all simply-connected 4-manifolds have this property.

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DOI : 10.5802/aif.3588
Classification : 57M12, 57M25
Keywords: 4-manifold, branched covering, trisection.
Mot clés : 4-variété, revêtement ramifiée, trisection.
Blair, Ryan 1 ; Cahn, Patricia 2 ; Kjuchukova, Alexandra 3 ; Meier, Jeffrey 4

1 Department of Mathematics and Statistics 1250 Bellflower Boulevard Long Beach, California 90840 (USA)
2 Department of Mathematics & Statistics Clark Science Center Smith College Burton Hall 115 Northampton, MA 01063 (USA)
3 Department of Mathematics University of Notre Dame 255 Hurley Bldg Notre Dame, IN 46556 (USA)
4 Department of Mathematics Western Washington University 516 High Street, Bellingham, WA 98229 (USA) 
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Blair, Ryan; Cahn, Patricia; Kjuchukova, Alexandra; Meier, Jeffrey. Note on three-fold branched covers of $S^4$. Annales de l'Institut Fourier, Online first, 18 p.

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