Twisted connected sums and special Riemannian holonomy
Differential Geometry
2007-05-23 v4
Abstract
We give a new, connected-sum-like construction of Riemannian metrics with special holonomy G_2 on compact 7-manifolds. The construction is based on a gluing theorem for appropriate elliptic partial differential equations. As a prerequisite, we also obtain asymptotically cylindrical Riemannian manifolds with holonomy SU(3) building up on the work of Tian and Yau. Examples of new topological types of compact 7-manifolds with holonomy G_2 are constructed using Fano 3-folds.
Keywords
Cite
@article{arxiv.math/0012189,
title = {Twisted connected sums and special Riemannian holonomy},
author = {Alexei Kovalev},
journal= {arXiv preprint arXiv:math/0012189},
year = {2007}
}
Comments
35 pages; v2: some technical corrections and clarifications, more general and systematic treatment of the examples; v3: technical corrections; v4: final version, error corrected in the fundamental group calculations in examples