The Riemannian geometry of the Yang-Mills moduli space |
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Authors: | David Groisser Thomas H Parker |
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Institution: | (1) Mathematics Department, State University of New York, 11794 Stony Brook, NY, USA;(2) Mathematics Department, Brandeis University, 02254 Waltham, MA, USA |
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Abstract: | The moduli space 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 1 ofk=1 instantons on the 4-sphere, and obtain an explicit formula for the metric in this case. In particular, we prove that 1 is rotationally symmetric and has finite geometry: it is an incomplete 5-manifold with finite diameter and finite volume.Partially supported by Horace Rackham Faculty Research Grant from the University of MichiganPartially supported by N.S.F. Grant DMS-8603461 |
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