Infinitely many new families of complete cohomogeneity one G$_2$-manifolds: G$_2$ analogues of the Taub–NUT and Eguchi–Hanson spaces

@article{Foscolo2018InfinitelyMN,
  title={Infinitely many new families of complete cohomogeneity one G\$\_2\$-manifolds: G\$\_2\$ analogues of the Taub–NUT and Eguchi–Hanson spaces},
  author={Lorenzo Foscolo and Mark S. Haskins and Johannes Nordstrom},
  journal={arXiv: Differential Geometry},
  year={2018}
}
We construct infinitely many new 1-parameter families of simply connected complete noncompact G_2-manifolds with controlled geometry at infinity. The generic member of each family has so-called asymptotically locally conical (ALC) geometry. However, the nature of the asymptotic geometry changes at two special parameter values: at one special value we obtain a unique member of each family with asymptotically conical (AC) geometry; on approach to the other special parameter value the family of… 

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