Compactified spaces of holomorphic curves in complex Grassmann manifolds

✍ Scribed by David E. Hurtubise; Marc D. Sanders

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 90 KB
• Volume: 109
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00153-4

✦ Synopsis

In this paper we study the topology of a compactification of the space of holomorphic maps of fixed degree from CP 1 into a finite-dimensional complex Grassmann manifold. We show that there is a homotopy equivalence through a range, increasing with the degree, between these compact spaces and an infinite-dimensional complex Grassmann manifold. These compact spaces form a direct system indexed by the degree, and the direct limit is homotopy equivalent to an infinite-dimensional complex Grassmann manifold.