Smooth \(Sp(2,\mathbf R)\)-actions on the 4-sphere
type: Item
instance of: scholarly article
title: Smooth \(Sp(2,\mathbf R)\)-actions on the 4-sphere
zbMATH Open document ID: 0890.57050
author: Kazuo Mukōyama
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1998-06-25T00:00:00Z
review text: The author constructs a one-to-one correspondence between the equivariant diffeomorphisms of smooth \(Sp(2,\mathbf R)\)-actions on standard 4-sphere without fixed points and the equivalence classes of certain pairs of \(\mathbf R\)-actions and maps defined on the circle subject to five conditions. This implies that there are infinitely many smooth \(Sp(2,\mathbf R)\)-actions on the sphere without fixed points up to equivariant diffeomorphism.
reviewed by: Vladimir L. Popov
Mathematics Subject Classification ID: 57S20
zbMATH DE Number: 1044140
zbMATH Keywords: sphere
zbMATH Keywords: fixed point
zbMATH Keywords: principal isotropy
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225298
OpenAlex ID: W2118322687
cites work: Compact transformation groups on \(Z_2\)-cohomology spheres with orbit of codimension 1
cites work: On smooth SL(2,\({\mathbb{C}})\) actions on 3-manifolds
cites work: Q5658847
cites work: Q3281164
cites work: A global formulation of the Lie theory of transformation groups
cites work: Real analytic SL(n,\({\mathbb{R}})\) actions on spheres
cites work: On smooth \(SO_ 0(p,q)\)-actions on \(S^{p+q-1}\)
DOI: 10.2748/TMJ/1178225298
description: scientific article; zbMATH DE number 1044140