Classification of real Nash fibre bundles

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• 作者：Francesco Guaraldo
• 关键词：Mathematics Subject Classification (2000) 32C05 ; 55P10 ; 55R10 ; 55R25 ; 55R35
• 刊名：Mathematische Zeitschrift
• 出版年：2008
• 出版时间：June, 2008
• 年：2008
• 卷：259
• 期：2
• 页码：311-319
• 全文大小：176.3 KB

文摘

Let G be a compact subgroup of an orthogonal group and X an affine, real, semialgebraic Nash variety. A principal Nash G-bundle over X is said to be strongly Nash if it is induced, up to Nash equivalences, of some universal bundle under a Nash map. Not all Nash bundles are strongly Nash and we denote by S(X, G) the class of strongly Nash G-bundles over X. The principal aim of this paper is to prove the following classification theorem: two bundles of S(X, G) are Nash equivalent if and only if they are topologically equivalent; more,there exists a bijection between the family of the classes of Nash equivalent bundles of S(X, G) and H1 (X, G_c)H^{1} (X, \mathcal G_c) , where G_c\mathcal G_c is the sheaf of germs of the continous maps from X to G. This result leads to find the largest class of principal Nash G-bundles over X in which the topological equivalence always implies the Nash one. Well, we prove that this class is exactly S(X, G).