The rank stable topology of instantons on $\overline {\mathbf {CP}}^2$
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- by Jim Bryan and Marc Sanders PDF
- Proc. Amer. Math. Soc. 125 (1997), 3763-3768 Request permission
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 $\ell _{\infty }$.References
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Additional Information
- Jim Bryan
- Affiliation: Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California 94720-5070
- ORCID: 0000-0003-2541-5678
- Email: jbryan@msri.org
- Marc Sanders
- Affiliation: Department of Mathematics and Computer Science, Dickinson College, Carlisle, Pennsylvania 17013
- Email: sandersm@dickinson.edu
- Received by editor(s): August 2, 1996
- Communicated by: Ronald A. Fintushel
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 3763-3768
- MSC (1991): Primary 58D27, 53C07, 55R45, 14Dxx
- DOI: https://doi.org/10.1090/S0002-9939-97-04156-7
- MathSciNet review: 1425114