Nash \(G\) manifold structures of compact or compactifiable \(C^ \infty G\) manifolds
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).
compactifiable \(C^ \infty G\) manifolds
scientific article; zbMATH DE number 952707