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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
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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Additional Information

Paul Norbury
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

Marc Sanders
Affiliation: Department of Mathematics, University of Minnesota, Minneapolis, Minneapolis, Minnesota 55455

Keywords: Instantons, Dirac operators, classifying space
Received by editor(s): January 13, 1995
Communicated by: Ronald Stern
Article copyright: © Copyright 1996 American Mathematical Society