Boundaries and complements of infinite- dimensional manifolds in the model space |
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Authors: | Katsuro Sakai |
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Institution: | Institute of Mathematics, University of Tsukuba, Sakura-mura, Ibaraki 305, Japan |
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Abstract: | Let M be a manifold modeled on a locally convex linear metric space E≌Eω (or ≌Eωf and N a Z-submanifold of M. Then N is collared in M. In this paper, we study the following problem 1, 3]: Under what conditions can M be embedded in E so that N is the topological boundary of M in E? We gain a more mild sufficient condition than the previous papers 7, 8] and a necessary and sufficient condition in the case M has the homotopy type of Sn (and each component of N is simply connected if n?2) and in the case N has the homotopy type of Sn (n?2). Also we obtain a necessary and sufficient condition under which M can be embedded in E so that bd M = N and cl(E\M) has the homotopy type of Sn (we assume that M and N are simply connected if n ? 2). |
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Keywords: | 57N20 57N35 58B05 embedding topological boundary |
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