The modulo 2 homology group of the space of rational functions
type: Item
instance of: scholarly article
title: The modulo 2 homology group of the space of rational functions
zbMATH Open document ID: 0703.55008
author: Yasuhiko Kamiyama
published in: Proceedings of the Japan Academy. Series A
publication date: 1990-01-01T00:00:00Z
review text: The cohomology group \(H_*(F_ k^*({\mathbb{S}}^ 2,{\mathbb{C}}{\mathbb{P}}^ m);{\mathbb{Z}}_ 2)\) of the space of based holomorphic maps of degree k from \({\mathbb{S}}^ 2\) to \({\mathbb{C}}{\mathbb{P}}^ m\) is considered. A series of theorems concerning certain elements of \(H_*(F_ k^*({\mathbb{S}}^ 2,{\mathbb{C}}{\mathbb{P}}^ m);{\mathbb{Z}}_ 2)\), produced by the loop sum and Dyer- Lashof operation, are proved. It is shown for different values of k and m that the elements considered are the basis of \(H_*(F_ k^*({\mathbb{S}}^ 2,{\mathbb{C}}{\mathbb{P}}^ m);{\mathbb{Z}}_ 2)\).
Mathematics Subject Classification ID: 55S12
Mathematics Subject Classification ID: 57R19
zbMATH DE Number: 4153470
zbMATH Keywords: cohomology group
zbMATH Keywords: holomorphic maps
zbMATH Keywords: Dyer-Lashof operation
reviewed by: Vyacheslav Abramov
MaRDI profile type: Publication
full work available at URL: pjaa.66.93
OpenAlex ID: W2095247064
cites work: Monopoles, non-linear \(\sigma\) models, and two-fold loop spaces
cites work: The homology of iterated loop spaces
cites work: The topology of spaces of rational functions
DOI: 10.3792/PJAA.66.93
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description: scientific article; zbMATH DE number 4153470