Compactified spaces of holomorphic curves in complex Grassmann manifolds

David Edward Hurtubise, Marc D. Sanders

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper we study the topology of a compactification of the space of holomorphic maps of fixed degree from ℂP1 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.

Original languageEnglish (US)
Pages (from-to)147-156
Number of pages10
JournalTopology and its Applications
Volume109
Issue number2
StatePublished - Dec 1 2001

Fingerprint

Holomorphic Curve
Grassmann Manifold
Complex Manifolds
Compact Space
Direct Limit
Homotopy Equivalence
Holomorphic Maps
Space Form
Compactification
Homotopy
Topology
Range of data

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

@article{0d212390c48b4498a1eee9dce3d2c8ee,
title = "Compactified spaces of holomorphic curves in complex Grassmann manifolds",
abstract = "In this paper we study the topology of a compactification of the space of holomorphic maps of fixed degree from ℂP1 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.",
author = "Hurtubise, {David Edward} and Sanders, {Marc D.}",
year = "2001",
month = "12",
day = "1",
language = "English (US)",
volume = "109",
pages = "147--156",
journal = "Topology and its Applications",
issn = "0166-8641",
publisher = "Elsevier",
number = "2",

}

Compactified spaces of holomorphic curves in complex Grassmann manifolds. / Hurtubise, David Edward; Sanders, Marc D.

In: Topology and its Applications, Vol. 109, No. 2, 01.12.2001, p. 147-156.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Compactified spaces of holomorphic curves in complex Grassmann manifolds

AU - Hurtubise, David Edward

AU - Sanders, Marc D.

PY - 2001/12/1

Y1 - 2001/12/1

N2 - In this paper we study the topology of a compactification of the space of holomorphic maps of fixed degree from ℂP1 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.

AB - In this paper we study the topology of a compactification of the space of holomorphic maps of fixed degree from ℂP1 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.

UR - http://www.scopus.com/inward/record.url?scp=0038258514&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038258514&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0038258514

VL - 109

SP - 147

EP - 156

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 2

ER -