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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Classifying spaces and Dirac operators coupled to instantons
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by Marc Sanders PDF
Trans. Amer. Math. Soc. 347 (1995), 4037-4072 Request permission

Abstract:

Let $M(k,SU(l))$ denote the moduli space of based gauge equivalence classes of $SU(l)$ instantons on principal bundles over ${S^4}$ with second Chern class equal to $k$. In this paper we use Dirac operators coupled to such connections to study the topology of these moduli spaces as $l$ increases relative to $k$. This "coupling" procedure produces maps ${\partial _u}:M(k,SU(l)) \to BU(k)$, and we prove that in the limit over $l$ such maps recover Kirwan’s $[\text {K}]$ homotopy equivalence $M(k,SU) \simeq BU(k)$. We also compute, for any $k$ and $l$, the image of the homology map ${({\partial _u})_ * }:{H_ * }(M(k,SU(l));Z) \to {H_ * }(BU(k);Z)$. Finally, we prove all the analogous results for $Sp(l)$ instantons.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 4037-4072
  • MSC: Primary 58D27; Secondary 55P99, 55R45, 57R57, 58G03
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1311915-7
  • MathSciNet review: 1311915