56 research outputs found
Homotopy types of homeomorphism groups of noncompact 2-manifolds
Suppose M is a noncompact connected PL 2-manifold and let H(M)_0 denote the
identity component of the homeomorphism group of M with the compact-open
topology. In this paper we classify the homotopy type of H(M)_0 by showing that
{\cal H}(M)_0 has the homotopy type of the circle if M is the plane, an open or
half open annulus, or the punctured projective plane. In all other cases we
show that H(M)_0 is homotopically trivial.Comment: 13 page
Spaces of embeddings of compact polyhedra into 2-manifolds
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,Sigma,sigma)-manifold, where E_K^LIP(X,M) and E_K^PL(X, M) denote the
subspaces of Lipschitz and PL embeddings.Comment: 13 page
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