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Canonical orientations for moduli spaces of G_2-instantons with gauge group SU(m) or U(m)

Abstract:

Suppose (X,g) is a compact, spin Riemannian 7-manifold, with Dirac operator D/g : 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 BE for the infinite-dimensional moduli space of connections on E, modulo gauge. There is a natural principal Z2-bundle OD/g → BE parametrizing orientations of E detD/gAdA for twisted elliptic operators D/gAdA at each [A] in BE. A theorem of Walpuski [33] shows OD/g is trivializable. We prove that if we choos...

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Publication status:
Accepted
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Lincoln College
Role:
Author
ORCID:
0000-0002-3530-8801
More by this author
Institution:
University of Oxford
Department:
Mathematical Institute
Role:
Author
Publisher:
International Press Publisher's website
EISSN:
1945-743X
ISSN:
0022-040X
Source identifiers:
938715
Language:
English
Keywords:
Pubs id:
pubs:938715
UUID:
uuid:84b6f229-8ef1-4095-b84f-62586ef0960d
Local pid:
pubs:938715
Deposit date:
2018-11-07

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