no. 1
Diffeomorphic souls and disconnected moduli spaces of nonnegatively curved metrics
[Sur les âmes difféomorphes et les espaces de modules de métriques à courbure non négative qui ne sont pas connexes]
Belegradek, Igor1 ; González-Álvaro, David2
1 School of Mathematics Georgia Institute of Technology Atlanta, GA, USA 30332
2 ETSI de Caminos, Canales y Puertos Universidad Politécnica de Madrid 28040, Spain
Annales de l'Institut Fourier, Tome 72 (2022) no. 1, pp. 109-122.

Nous donnons des exemples de variétés ouvertes qui admettent une infinité de métriques complètes à courbure sectionnelle non négative telles que leurs âmes soient identiques et que leurs classes d’équivalence se trouvent dans des composantes connexes différentes de l’espace de modules. Tous les exemples de ce genre, connus auparavant, ont une âme de codimension un. Dans les exemples que nous présentons, les âmes sont de codimension trois et deux.

We give examples of open manifolds that carry infinitely many complete metrics of nonnegative sectional curvature such that they all have the same soul, and their isometry classes lie in different connected components of the moduli space. All previously known examples of this kind have souls of codimension one. In our examples the souls have codimensions three and two.

Reçu le :
Révisé le :
Accepté le :
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DOI : 10.5802/aif.3471
Classification : 53C20
Keywords: Nonnegative curvature, soul, moduli space, positive scalar curvature.
Mot clés : Courbure non négative, âme, espace de module, courbure scalaire positive

Belegradek, Igor 1 ; González-Álvaro, David 2

1 School of Mathematics Georgia Institute of Technology Atlanta, GA, USA 30332
2 ETSI de Caminos, Canales y Puertos Universidad Politécnica de Madrid 28040, Spain
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     author = {Belegradek, Igor and Gonz\'alez-\'Alvaro, David},
     title = {Diffeomorphic souls and disconnected moduli spaces of nonnegatively curved metrics},
     journal = {Annales de l'Institut Fourier},
     pages = {109--122},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {72},
     number = {1},
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Belegradek, Igor; González-Álvaro, David. Diffeomorphic souls and disconnected moduli spaces of nonnegatively curved metrics. Annales de l'Institut Fourier, Tome 72 (2022) no. 1, pp. 109-122. doi : 10.5802/aif.3471. https://aif.centre-mersenne.org/articles/10.5802/aif.3471/

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