2021/01/25 by Lehmann, Fabian
#53C25 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2101.10310
We consider the moduli space Mν of torsion-free, asymptotically conical (AC) Spin(7)-structures which are defined on the same manifold and asymptotic to the same Spin(7)-cone with decay rate ν<0. We show that Mν is an orbifold if ν is a generic rate in the non-L2 regime (-4,0). Infinitesimal deformations are given by topological data and solutions to a non-elliptic first-order PDE system on the compact link of the asymptotic cone. As an application, we show that the classical Bryant-Salamon metric on the bundle of positive spinors on S4 has no continuous deformations as an AC Spin(7)-metric.