Immersions of real projective spaces into complex projective spaces
type: Item
instance of: scholarly article
title: Immersions of real projective spaces into complex projective spaces
zbMATH Open document ID: 0658.57018
author: Tsutomu Yasui
published in: Hiroshima Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: This paper achieves a classification up to regular homotopy of immersions from a real projective space \(P^ n({\mathbb{R}})\) into a complex projective space \(P^ m({\mathbb{C}})\). Calculations with characteristic classes show that, for \(n>m\), any such immersion is nullhomotopic. For \(n\leq m\), both homotopy classes can be realized by immersions, the non-trivial one by the natural embedding. Since \(\pi_ 1\) of the relevant mapping space is trivial, the classification up to regular homotopy of all immersions in a given homotopy class is as for immersions into \({\mathbb{R}}^{2m}\).
Mathematics Subject Classification ID: 57R42
Mathematics Subject Classification ID: 55Q52
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 4076084
zbMATH Keywords: immersions from a real projective space into a complex projective space
zbMATH Keywords: regular homotopy
zbMATH Keywords: characteristic classes
reviewed by: Martin Raussen
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4076084