Lie algebra bundles and a generalization of Lie group bundles
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We de ne top space bundle as a generalization of Lie group bundle. Top space bundle is a smooth bre bundle whose bres are top spaces - a generalization of Lie groups. In this paper we generalize many results on top spaces to a class of top space bundles whose bres have nitely many identities. Further, we de ne the Lie algebra bundle of a top space bundle and answer a natural question `does there exist a top space bundle (that is not a Lie group bundle) whose Lie algebra bundle is isomorphic to the given one?' by revisiting the techniques of Douady and Lazard.
Abstract
We de ne top space bundle as a generalization of Lie group bundle. Top space bundle is a smooth bre bundle whose bres are top spaces - a generalization of Lie groups. In this paper we generalize many results on top spaces to a class of top space bundles whose bres have nitely many identities. Further, we de ne the Lie algebra bundle of a top space bundle and answer a natural question `does there exist a top space bundle (that is not a Lie group bundle) whose Lie algebra bundle is isomorphic to the given one?' by revisiting the techniques of Douady and Lazard.
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