Actions of symplectic groups on certain manifolds
type: Item
instance of: scholarly article
title: Actions of symplectic groups on certain manifolds
zbMATH Open document ID: 0542.57028
author: Aiko Nakanishi
author: Fuichi Uchida
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1984-01-01T00:00:00Z
review text: This paper studies smooth nontrivial actions of Sp(n), \(n\geq 7\), on a closed manifold X having the cohomology ring of a product \(P_ a({\mathbb{C}})\times P_ b({\mathbb{C}})\) or \(P_ a({\mathbb{H}})\times P_ b({\mathbb{C}})\) of complex or quaternionic projective spaces. A typical result says that if \(X\sim P_ a({\mathbb{C}})\times P_ b({\mathbb{C}})\) with 1\(\leq b\leq 4\leq 2n\) and \(a+b\leq 4n-3\), then \(a=2n-1\) and \(X=P_{2n- 1}({\mathbb{C}})\times Y\) where Sp(n) acts in the usual way on \(P_{2n- 1}({\mathbb{C}})\) and trivially on Y, with Y having the cohomology ring structure of \(P_ b({\mathbb{C}})\).
Mathematics Subject Classification ID: 57S15
Mathematics Subject Classification ID: 57S25
zbMATH DE Number: 3862067
zbMATH Keywords: smooth actions of the symplectic group on a closed manifold having the cohomology ring of a product of complex or quaternionic projective spaces
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228905
OpenAlex ID: W1975965390
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DOI: 10.2748/TMJ/1178228905
description: scientific article; zbMATH DE number 3862067