Nash \(G\) manifold structures of compact or compactifiable \(C^ \infty G\) manifolds
type: Item
instance of: scholarly article
title: Nash \(G\) manifold structures of compact or compactifiable \(C^ \infty G\) manifolds
zbMATH Open document ID: 0879.58002
author: Tomohiro Kawakami
published in: Journal of the Mathematical Society of Japan
publication date: 1998-01-25T00:00:00Z
review text: Let \(G\) be a compact affine Nash group. A \(C^\infty G\) manifold \(X\) is said to admit a (resp. an affine, a nonaffine) Nash \(G\) manifold structure if there exists a (resp. an affine, a nonaffine) Nash \(G\) manifold \(Y\) such that \(X\) is \(C^\infty G\) diffeomorphic to \(Y\). A \(C^\infty G\) manifold \(X\) is said to be compactifiable as a \(C^\infty G\) manifold if there exists a compact \(C^\infty G\) manifold \(Y\) with boundary so that \(X\) is \(C^\infty G\) diffeomorphic to the interior of \(Y\). The present paper consists of two parts. In the first part the author investigates Nash \(G\) manifold structures of compact \(C^\infty G\) manifolds (see Theorem 1). In the second part the author studies Nash \(G\) manifold structures of compactifiable (noncompact) \(C^\infty G\) manifolds (see Theorem 2).
Mathematics Subject Classification ID: 58A07
Mathematics Subject Classification ID: 14P20
zbMATH DE Number: 952707
zbMATH Keywords: compactifiable \(C^ \infty G\) manifolds
zbMATH Keywords: Nash \(G\) manifold structures
zbMATH Keywords: compact \(C^ \infty G\) manifolds
reviewed by: Neculai Papaghiuc
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04820321
OpenAlex ID: W2019929759
DOI: 10.2969/JMSJ/04820321
description: scientific article; zbMATH DE number 952707