Geodesic
Heegaard splittings of (surface) x I are standars.
Mathematische Annalen, Tome 295 (1993) no. 1, pp. 549-564.

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Mots-clés : Heegaard splittings of a closed orientable genus surface crossed with an interval, compression bodies, spines 
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     author = {Martin Scharlemann and Abigail Thompson},
     title = {Heegaard splittings of (surface) x {I} are standars.},
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Martin Scharlemann; Abigail Thompson. Heegaard splittings of (surface) x I are standars.. Mathematische Annalen, Tome 295 (1993) no. 1, pp. 549-564. http://geodesic.mathdoc.fr/item/MAN_1993__295_1_165057/