کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9516792 | 1633122 | 2005 | 34 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Homotopy types of the components of spaces of embeddings of compact polyhedra into 2-manifolds
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Suppose M is a connected PL 2-manifold and X is a compact connected subpolyhedron of M (Xâ 1 pt, a closed 2-manifold). Let E(X,M) denote the space of topological embeddings of X into M with the compact-open topology and let E(X,M)0 denote the connected component of the inclusion iX:XâM in E(X,M). In this paper we classify the homotopy type of E(X,M)0 in terms of the subgroup G=Im[iXâ:Ï1(X)âÏ1(M)]. We show that if G is not a cyclic group and MâT2, K2 then E(X,M)0ââ, if G is a nontrivial cyclic group and MâP2, T2, K2 then E(X,M)0âS1, and when G=1, if X is an arc or M is orientable then E(X,M)0âST(M) and if X is not an arc and M is nonorientable then E(X,M)0âST(MË). Here S1 is the circle, T2 is the torus, P2 is the projective plane and K2 is the Klein bottle. The symbol ST(M) denotes the tangent unit circle bundle of M with respect to any Riemannian metric of M and when M is nonorientable, MË denotes the orientable double cover of M.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 153, Issues 2â3, 1 September 2005, Pages 174-207
Journal: Topology and its Applications - Volume 153, Issues 2â3, 1 September 2005, Pages 174-207
نویسندگان
Tatsuhiko Yagasaki,