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The Riemannian geometry of the Yang-Mills moduli space

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Abstract

The moduli space ℳ of self-dual connections over a Riemannian 4-manifold has a natural Riemannian metric, inherited from theL 2 metric on the space of connections. We give a formula for the curvature of this metric in terms of the relevant Green operators. We then examine in great detail the moduli space ℳ1 ofk=1 instantons on the 4-sphere, and obtain an explicit formula for the metric in this case. In particular, we prove that ℳ1 is rotationally symmetric and has “finite geometry:” it is an incomplete 5-manifold with finite diameter and finite volume.

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Authors and Affiliations

  1. Mathematics Department, State University of New York, 11794, Stony Brook, NY, USA

    David Groisser

  2. Mathematics Department, Brandeis University, 02254, Waltham, MA, USA

    Thomas H. Parker

Authors
  1. David Groisser
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  2. Thomas H. Parker
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Additional information

Communicated by C. H. Taubes

Partially supported by Horace Rackham Faculty Research Grant from the University of Michigan

Partially supported by N.S.F. Grant DMS-8603461

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Groisser, D., Parker, T.H. The Riemannian geometry of the Yang-Mills moduli space. Commun.Math. Phys. 112, 663–689 (1987). https://doi.org/10.1007/BF01225380

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  • DOI: https://doi.org/10.1007/BF01225380

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