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Orientability of moduli spaces of Spin(7)-instantons

Abstract:

Suppose (X,Ω,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 BP of all connections on P modulo gauge is orientable, in a certain sense. We deduce that the moduli space MSpin(7) ⊂ BP of irreducible Spin(7)-instanton connections on P modulo P gauge, as a manifold or derived manifold, is orientable. This improves theorems of C...

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Publication status:
Not Published
Peer review status:
Not Peer reviewed
Version:
Author's Original

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Lincoln College
ORCID:
0000-0002-3530-8801
Pubs id:
pubs:946579
URN:
uri:22804816-5e94-4a6e-9a98-db0ad77c15ce
UUID:
uuid:22804816-5e94-4a6e-9a98-db0ad77c15ce
Local pid:
pubs:946579

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