Gauge theory, calibrated geometry and harmonic spinors

Jan, 2011
17 pages
Published in:
  • J.Lond.Math.Soc. 86 (2012) 2, 482-498
  • Published: Oct 1, 2012
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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