Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds

摘要

Suppose (X, Omega, g) is a compact Spin(7)-manifold, e.g. a Riemannian 8-manifold with holonomy Spin(7), or a Calabi-Yau 4-fold. Let G be U(m) or SU(m), and P -> X be a principal G-bundle. We show that the infinite-dimensional moduli space B-P of all connections on P modulo gauge is orientable, in a certain sense. We deduce that the moduli space M-P(Spin(7)) subset of B-P of irreducible Spin(7)-instanton connections on P modulo gauge, as a manifold or derived manifold, is orientable. This improves theorems of Cao and Leung [0] and Munoz and Shahbazi [42].