Gauge theory, calibrated geometry and harmonic spinors
Jan, 201117 pages
Published in:
- J.Lond.Math.Soc. 86 (2012) 2, 482-498
- Published: Oct 1, 2012
e-Print:
- 0902.3738 [math.DG]
DOI:
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Abstract: (London Mathematical Society)
In this paper, connections between different gauge-theoretical problems in high and low dimensions are established. In particular, it is shown that higher dimensional anti-self-duality equations on the total spaces of spinor bundles over low-dimensional manifolds can be interpreted as the Taubes–Pidstrygach generalization of the Seiberg–Witten equations. By collapsing each fibre of the spinor bundle to a point, solutions of the Taubes–Pidstrygach equations are related to generalized harmonic spinors. This approach is also generalized to arbitrary fibrations (without singular fibres) compatible with an appropriate calibration.Note:
- 20pp., exposition changed,typos corrected
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