@techreport{fdd13f91fd0e4a0e9aef61814eddddcb,

title = "An analytic invariant of G2 manifolds",

abstract = "The first and third authors have constructed a defect invariant nu in Z/48 for G_2-structures on a closed 7-manifold. We describe the nu-invariant using eta-invariants and Mathai-Quillen currents on M and show that it can be refined to an integer-valued invariant bar nu for G_2-holonomy metrics. As an example, we determine the bar nu invariants of twisted and extra twisted connected sums a la Kovalev, Corti-Haskins-Nordstr{\"o}m-Pacini, and Nordstr{\"o}m. In particular, we exhibit examples of 7-manifolds where the moduli space of G_2-holonomy metrics has at least two connected components. In one of these examples, the underlying G_2-structures are homotopic, in another one, they are not.",

keywords = "math.GT, math.DG, 57R20 (Primary) 53C29, 58J28 (Secondary)",

author = "Diarmuid Crowley and Sebastian Goette and Johannes Nordstr{\"o}m",

note = "Submitted to Inventiones Mathematicae. pdfLaTeX, 26 pages, 2 figures (tikz)",

year = "2020",

month = nov,

day = "3",

language = "English",

series = "arXiv",

publisher = "Cornell University",

type = "WorkingPaper",

institution = "Cornell University",

}