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The rank stable topology of instantons on $\overline{\mathbf{CP}}^2$

Authors: Jim Bryan and Marc Sanders
Journal: Proc. Amer. Math. Soc. 125 (1997), 3763-3768
MSC (1991): Primary 58D27, 53C07, 55R45, 14Dxx
MathSciNet review: 1425114
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Abstract: Let $% \mathcal{M} _{k}^{n}$ be the moduli space of based (anti-self-dual) instantons on $% \overline{\mathbf {CP}}^2$ of charge $k$ and rank $n$. There is a natural inclusion $% \mathcal{M} _{k}^{n}\hookrightarrow % \mathcal{M}_{k}^{n+1}$. We show that the direct limit space $% \mathcal{M}_k^\infty$ is homotopy equivalent to $BU(k)\times BU(k)$. Let $% \ell _{\infty}$ be a line in the complex projective plane and let $% \widetilde{% {\mathbf C} % {\mathbf{P}}}^{2}$ be the blow-up at a point away from $% \ell _{\infty}$. $% \mathcal{M} _{k}^{n}$ can be alternatively described as the moduli space of rank $n$ holomorphic bundles on $% \widetilde{% \mathbf{C}% \mathbf{P}}^{2}$ with $c_{1}=0$ and $c_{2}=k$ and with a fixed holomorphic trivialization on $% \ell _{\infty}$.

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Additional Information

Jim Bryan
Affiliation: Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California 94720-5070

Marc Sanders
Affiliation: Department of Mathematics and Computer Science, Dickinson College, Carlisle, Pennsylvania 17013

Received by editor(s): August 2, 1996
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1997 American Mathematical Society

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