Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58D27, 53C07, 55R45, 14Dxx

Retrieve articles in all journals with MSC (1991): 58D27, 53C07, 55R45, 14Dxx

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

PII: S 0002-9939(97)04156-7
Received by editor(s): August 2, 1996
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1997 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia