@techreport{86175b48d9634cb6825c3e12c328c8bc,

title = "Complete non-compact G2-manifolds from asymptotically conical Calabi-Yau 3-folds",

abstract = "We develop a powerful new analytic method to construct complete non-compact G2-manifolds, i.e. Riemannian 7-manifolds (M,g) whose holonomy group is the compact exceptional Lie group G2. Our construction starts with a complete non-compact asymptotically conical Calabi-Yau 3-fold B and a circle bundle M over B satisfying a necessary topological condition. Our method then produces a 1-parameter family of circle-invariant complete G2-metrics on M that collapses to the original Calabi-Yau metric on the base B as the parameter converges to 0. The G2-metrics we construct have controlled asymptotic geometry at infinity, so-called asymptotically locally conical (ALC) metrics, and are the natural higher-dimensional analogues of the ALF metrics that are well known in 4-dimensional hyperk\{"}ahler geometry. We give two illustrations of the strength of our method. Firstly we use it to construct infinitely many diffeomorphism types of complete non-compact simply connected G2-manifolds; previously only a handful of such diffeomorphism types was known. Secondly we use it to prove the existence of continuous families of complete non-compact G2-metrics of arbitrarily high dimension; previously only rigid or 1-parameter families of complete non-compact G2-metrics were known.",

keywords = "math.DG, hep-th, 53C10, 53C25, 53C29, 53C80",

author = "Lorenzo Foscolo and Mark Haskins and Johannes Nordstrom",

note = "Duke Mathematical Journal Publisher name: Duke University Press ISSN (Print): 0012-7094 Acceptance date8 Dec 2020",

year = "2020",

month = dec,

day = "28",

language = "English",

series = "Arxiv",

type = "WorkingPaper",

}