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Metrics and convergence in moduli spaces of maps
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 27 (2018) no. 3, pp. 497-526.

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.

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.

Received:
Accepted:
Published online:
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.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     author = {Joseph Palmer},
     title = {Metrics and convergence in moduli spaces of maps},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {497--526},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 27},
     number = {3},
     year = {2018},
     doi = {10.5802/afst.1577},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1577/}
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Joseph Palmer. Metrics and convergence in moduli spaces of maps. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 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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