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Spaces of embeddings of compact polyhedra into 2-manifolds

✍ Scribed by Tatsuhiko Yagasaki

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
186 KB
Volume
108
Category
Article
ISSN
0166-8641

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✦ Synopsis

Let M be a PL 2-manifold and X be a compact subpolyhedron of M and let E (X, M) denote the space of embeddings of X into M with the compact-open topology. In this paper we study an extension property of embeddings of X into M and show that the restriction map from the homeomorphism group of M to E (X, M) is a principal bundle. As an application we show that if M is a Euclidean PL 2-manifold and dim X 1 then the triple (E (X, M), E LIP (X, M), E PL (X, M)) is an (s, Ξ£, Οƒ )-manifold, where E LIP K (X, M) and E PL K (X, M) denote the subspaces of Lipschitz and PL embeddings.

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