An analytic invariant of G2 manifolds

• 成果类型: Article
• 署名作者: Crowley, Diarmuid; Goette, Sebastian; Nordstrom, Johannes
• 署名单位: University of Melbourne; University of Freiburg; University of Bath
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01310-z
• 发表日期: 2025
• 页码: 865-907
• 关键词: spectral flow; eta-invariant; maslov index

摘要

We prove that the moduli space of holonomy G2-metrics on a closed 7-manifold can be disconnected by presenting a number of explicit examples. We detect different connected components of the G2-moduli space by defining an analytic refinement nu(M, g). Z of the defect invariant nu(M,phi)is an element of Z/48-structures. on a closed 7-manifold M introduced by the first and third authors. The nu-invariant is defined using.-invariants and Mathai-Quillen currents on M and we compute it for twisted connected sums a la Kovalev, Corti-Haskins-Nordstrom-Pacini and extra-twisted connected sums as constructed by the second and third authors. In particular, we find examples of G2-holonomy metrics in different components of the moduli space where the associated G2-structures are homotopic and other examples where they are not.