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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: Let $M(k,SO(n))$ be the moduli space of based gauge equivalence classes of $SO(n)$ instantons on principal $SO(n)$ bundles over $S^4$ with first Pontryagin class $p_1=2k$. 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 $n$, the moduli space is homotopy equivalent to the classifying space $BSp(k)$. Finally, we use Dirac operators coupled to such connections to exhibit a particular and quite natural homotopy equivalence.


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  • [ADHM] M.F. Atiyah, V. G. Drinfeld, N.J. Hitchin and Y. I. Manin, Construction of instantons, Phys. Lett. A, 65 (1978), 185-187. MR 82g:81049
  • [AJ] M.F. Atiyah and J.D.S. Jones, Topological aspects of Yang-Mills theory, Comm. Math. Phys. 61 (1978), 97-118. MR 80j:58021
  • [AHS] M.F. Atiyah, N.J. Hitchin, and I.M. Singer, Self-duality in four dimensional Riemannian Geometry, Proc. of Royal Society London, A 362 (1978), 425-461. MR 80d:53023
  • [D] S.K. Donaldson, Instantons and geometric invariant theory, Comm. Math. Phys., 93 (1984), 453-460. MR 86m:32043
  • [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
  • [Ti] Y. Tian, The Atiyah-Jones Conjecture for Classical Groups, preprint.

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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

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