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Canonical orientations for moduli spaces of G2-instantons with gauge group SU(m) or U(m)

Abstract:

Suppose (X, g) is a compact, spin Riemannian 7-manifold, with Dirac operator D : C∞(X, S) → C∞(X, S). Let G be SU(m) or U(m), and E → X be a rank m complex bundle with G-structure. Write B_E for the infinite-dimensional moduli space of connections on E, modulo gauge. There is a natural principal Z_2 -bundle O^D → B_E parametrizing orientations of det D_{Ad A} for twisted elliptic operators D_{Ad A} at each [A] in B_E. A theorem of Walpuski shows O is trivializable. We prove that if we choose ...

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Not Published
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Not peer reviewed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
Role:
Author
ORCID:
0000-0002-3530-8801
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
Pubs id:
pubs:938715
URN:
uri:84b6f229-8ef1-4095-b84f-62586ef0960d
UUID:
uuid:84b6f229-8ef1-4095-b84f-62586ef0960d
Local pid:
pubs:938715

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