We construct many new topological types of compact G(2)-manifolds, that is, Riemannian 7-manifolds with holonomy group G(2). To achieve this we extend the twisted connected sum construction first developed by Kovalev and apply it to the large class of asymptotically cylindrical Calabi-Yau 3-folds built from semi-Fano 3-folds constructed previously by the authors. In many cases we determine the diffeomorphism type of the underlying smooth 7-manifolds completely; we find that many 2-connected 7-manifolds can be realized as twisted connected sums in a variety of ways, raising questions about the global structure of the moduli space of G(2)-metrics. Many of the G(2)-manifolds we construct contain compact rigid associative 3-folds, which play an important role in the higher-dimensional enumerative geometry (gauge theory/calibrated submanifolds) approach to defining deformation invariants of G(2)-metrics. By varying the semi-Fanos used to build different G(2)-metrics on the same 7-manifold we can change the number of rigid associative 3-folds we produce.

G_2-manifolds and associative submanifolds via semi-Fano 3-folds

PACINI, TOMMASO
2015

Abstract

We construct many new topological types of compact G(2)-manifolds, that is, Riemannian 7-manifolds with holonomy group G(2). To achieve this we extend the twisted connected sum construction first developed by Kovalev and apply it to the large class of asymptotically cylindrical Calabi-Yau 3-folds built from semi-Fano 3-folds constructed previously by the authors. In many cases we determine the diffeomorphism type of the underlying smooth 7-manifolds completely; we find that many 2-connected 7-manifolds can be realized as twisted connected sums in a variety of ways, raising questions about the global structure of the moduli space of G(2)-metrics. Many of the G(2)-manifolds we construct contain compact rigid associative 3-folds, which play an important role in the higher-dimensional enumerative geometry (gauge theory/calibrated submanifolds) approach to defining deformation invariants of G(2)-metrics. By varying the semi-Fanos used to build different G(2)-metrics on the same 7-manifold we can change the number of rigid associative 3-folds we produce.
164
10
1971
2092
https://arxiv.org/pdf/1207.4470v3
https://arxiv.org/abs/1207.4470v3
CALABI-YAU 3-FOLDS, COMPACT RIEMANNIAN 7-MANIFOLDS, EXCEPTIONAL HOLONOMY, MANIFOLDS, CLASSIFICATION, KAHLER,DEFORMATIONS, G(2), DESINGULARIZATIONS, SINGULARITIES
Corti Alessio; Haskins Mark; Nordstrom Johannes; Pacini Tommaso
File in questo prodotto:
File Dimensione Formato  
euclid.dmj.1436909416.pdf

Accesso riservato

Descrizione: articolo pubblicato
Tipo di file: PDF EDITORIALE
Dimensione 767.23 kB
Formato Adobe PDF
767.23 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pacini.pdf

Accesso riservato

Tipo di file: PDF EDITORIALE
Dimensione 1.03 MB
Formato Adobe PDF
1.03 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1616213
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 70
  • ???jsp.display-item.citation.isi??? 59
social impact