Asymptotically cylindrical 7-manifolds of holonomy G_2 with applications to compact irreducible G_2-manifolds

Details Asymptotically cylindrical 7-manifolds of holonomy G_2 with applications to compact irreducible G_2-manifolds Asymptotically cylindrical 7-manifolds of holonomy G_2 with applications to compact irreducible G_2-manifolds

2009-07-03

arxiv.org/abs/0907.0497v4

Ann. Global Anal. Geom. 38 (2010), 221-257

Mathematics

Differential Geometry

36 pages; v2: corrected trivial typos; v3: some arguments corrected and improved; v4: a number of improvements on presentation

Scientific paper

10.1007/s10455-010-9210-8

We construct examples of exponentially asymptotically cylindrical Riemannian 7-manifolds with holonomy group equal to G_2. To our knowledge, these are the first such examples. We also obtain exponentially asymptotically cylindrical coassociative calibrated submanifolds. Finally, we apply our results to show that one of the compact G_2-manifolds constructed by Joyce by desingularisation of a flat orbifold T^7/\Gamma can be deformed to one of the compact G_2-manifolds obtainable as a generalized connected sum of two exponentially asymptotically cylindrical SU(3)-manifolds via the method given by the first author (math.DG/0012189).

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