September 13, 2021
TITLE: Non-compact Spin(7)-manifolds
In the non-compact setting, symmetry reduction methods can be used to simplify the condition for Spin(7)-holonomy, which in general is given by a large, non-linear, first order PDE system, to a system of ODEs. I will talk about a particular example with symmetry group SU(3). I will outline a rigorous proof for the existence of two families of complete Spin(7)-metrics, where all members are either asymptotically locally conical (ALC), or asymptotically conical (AC).
These families were conjectured to exist earlier and fit into the landscape of other known families of non-compact G2 and Spin(7) holonomy spaces. Time permitting, I will also discuss the deformation theory of AC Spin(7)-manifolds. The talk is based on arXiv:2012.11758 and arXiv:2101.10310.