Feuilleter
no. 3
Metrics and convergence in moduli spaces of maps
Joseph Palmer1
1 University of California, San Diego, Mathematics Department, 9500 Gilman Drive, #0112, La Jolla, CA 92093-0112, USA.
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 27 (2018) no. 3, pp. 497-526.

Nous présentons un cadre général pour l’étude de la convergence des familles d’applications entre variétés dont les domaines de définition sont distincts. Étant données deux variétés M et N, M étant munie d’une forme volume, nous considérons des familles d’applications dans l’ensemble {(φ,B φ )∣B φ ⊂M,φ:B φ →NavecB φ ,φmesurable} et nous définissons une distance sur cet ensemble, de type distance L 1 généralisée. Nous démontrons que l’espace métrique ainsi obtenu est toujours complet. Nous nous concentrons ensuite sur l’étude des propriétés de convergence de telles familles d’applications.

We provide a general framework to study convergence properties of families of maps between manifolds which have distinct domains. For manifolds M and N where M is equipped with a volume form we consider families of maps in the collection {(φ,B φ )∣B φ ⊂M,φ:B φ →NwithB φ ,φbothmeasurable} and we define a distance function similar to a generalized L 1 distance on such a collection. We show that the resulting metric space is always complete. We then shift our focus to exploring the convergence properties of families of such maps.

Reçu le :
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DOI : 10.5802/afst.1577

Joseph Palmer 1

1 University of California, San Diego, Mathematics Department, 9500 Gilman Drive, #0112, La Jolla, CA 92093-0112, USA.
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Joseph Palmer. Metrics and convergence in moduli spaces of maps. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 27 (2018) no. 3, pp. 497-526. doi : 10.5802/afst.1577. https://afst.centre-mersenne.org/articles/10.5802/afst.1577/

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