Real instantons, Dirac operators and quaternionic classifying spaces
Authors:
Paul Norbury and Marc Sanders
Journal:
Proc. Amer. Math. Soc. 124 (1996), 2193-2201
MSC (1991):
Primary 53C07, 55P38; Secondary 55R45
DOI:
https://doi.org/10.1090/S0002-9939-96-03358-8
MathSciNet review:
1327032
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be the moduli space of based gauge equivalence classes of
instantons on principal
bundles over
with first Pontryagin class
. In this paper, we use a monad description (Y. Tian, The Atiyah-Jones conjecture for classical groups, preprint, S. K. Donaldson, Comm. Math. Phys. 93 (1984), 453--460) of these moduli spaces to show that in the limit over
, the moduli space is homotopy equivalent to the classifying space
. Finally, we use Dirac operators coupled to such connections to exhibit a particular and quite natural homotopy equivalence.
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- [AJ] M. F. Atiyah and J. D. S. Jones, Topological aspects of Yang-Mills theory, Comm. Math. Phys. 61 (1978), no. 2, 97–118. MR 503187
- [AHS] M. F. Atiyah, N. J. Hitchin, and I. M. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A 362 (1978), no. 1711, 425–461. MR 506229, https://doi.org/10.1098/rspa.1978.0143
- [D] S. K. Donaldson, Instantons and geometric invariant theory, Comm. Math. Phys. 93 (1984), no. 4, 453–460. MR 763753
- [K] F. Kirwan, Geometric Invariant Theory and the Atiyah-Jones conjecture, Proceedings of the Sophus Lie Memorial Conference (Oslo, 1992), editors O.A. Laudal and B. Jahren, Scandinavian University Press, 1994, 161-188.
- [S] M. Sanders, Classifying spaces and Dirac operators coupled to instantons, Transactions of the American Mathematical Society 347 (1995), 4037--4072. CMP 95:15
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Additional Information
Paul Norbury
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Email:
norbs@maths.warwick.ac.uk
Marc Sanders
Affiliation:
Department of Mathematics, University of Minnesota, Minneapolis, Minneapolis, Minnesota 55455
Email:
sanders@math.umn.edu
DOI:
https://doi.org/10.1090/S0002-9939-96-03358-8
Keywords:
Instantons,
Dirac operators,
classifying space
Received by editor(s):
January 13, 1995
Communicated by:
Ronald Stern
Article copyright:
© Copyright 1996
American Mathematical Society