TY - JOUR
T1 - Asymptotically cylindrical 7-manifolds of holonomy G2 with applications to compact irreducible G2-manifolds
AU - Kovalev, Alexei
AU - Nordström, Johannes
PY - 2010/10/1
Y1 - 2010/10/1
N2 - We construct examples of exponentially asymptotically cylindrical (EAC) Riemannian 7-manifolds with holonomy group equal to G2. To our knowledge, these are the first such examples. We also obtain EAC coassociative calibrated submanifolds. Finally, we apply our results to show that one of the compact G2-manifolds constructed by Joyce by desingularisation of a flat orbifold T7/Γ can be deformed to give one of the compact G2-manifolds obtainable as a generalized connected sum of two EAC SU(3)-manifolds via the method of Kovalev (J Reine Angew Math 565:125-160, 2003).
AB - We construct examples of exponentially asymptotically cylindrical (EAC) Riemannian 7-manifolds with holonomy group equal to G2. To our knowledge, these are the first such examples. We also obtain EAC coassociative calibrated submanifolds. Finally, we apply our results to show that one of the compact G2-manifolds constructed by Joyce by desingularisation of a flat orbifold T7/Γ can be deformed to give one of the compact G2-manifolds obtainable as a generalized connected sum of two EAC SU(3)-manifolds via the method of Kovalev (J Reine Angew Math 565:125-160, 2003).
UR - http://www.scopus.com/inward/record.url?scp=77956720987&partnerID=8YFLogxK
UR - http://arxiv.org/abs/0907.0497
UR - http://dx.doi.org/10.1007/s10455-010-9210-8
U2 - 10.1007/s10455-010-9210-8
DO - 10.1007/s10455-010-9210-8
M3 - Article
SN - 0232-704X
VL - 38
SP - 221
EP - 257
JO - Annals of Global Analysis and Geometry
JF - Annals of Global Analysis and Geometry
IS - 3
ER -