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

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) P ⊂ BP of irreducible Spin(7)-instanton connections on P modulo gauge, as a manifold or derived manifold, is orientable. This improves theorems of...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.aim.2020.107134

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0002-3530-8801
Publisher:
Elsevier Publisher's website
Journal:
Advances in Mathematics Journal website
Volume:
368
Article number:
107134
Publication date:
2020-04-15
Acceptance date:
2020-04-01
DOI:
EISSN:
1090-2082
ISSN:
0001-8708
Language:
English
Keywords:
Pubs id:
1096654
Local pid:
pubs:1096654
Deposit date:
2020-03-26

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