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S.Gadgil, On the geometric simple connectivity of open manifolds
 I.M.R.N
"... A manifold is said to be geometrically simply connected if it has a proper handle decomposition without 1handles. By the work of Smale, for compact manifolds of dimension at least five, this is equivalent to simpleconnectivity. We prove that there exists an obstruction to an open simply connected ..."
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Cited by 12 (8 self)
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A manifold is said to be geometrically simply connected if it has a proper handle decomposition without 1handles. By the work of Smale, for compact manifolds of dimension at least five, this is equivalent to simpleconnectivity. We prove that there exists an obstruction to an open simply connected nmanifold of dimension n ≥ 5 being geometrically simply connected. In particular, for each n ≥ 4 there exist uncountably many simply connected nmanifolds which are not geometrically simply connected. We also prove that for n ̸ = 4 an nmanifold proper homotopy equivalent to a weakly geometrically simply connected polyhedron is geometrically simply connected (for n = 4 it is only end compressible). We analyze further the case n = 4 and Poénaru’s conjecture.
On Proper Homotopy Type and the Simple Connectivity At Infinity of Open 3Manifolds
, 2000
"... The main result of this note is that an open simply connected 3manifold W³ proper homotopically dominated by a weak geometrically simply connected polyhedron is simply connected at infinity. This generalizes the main result of [16]. ..."
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Cited by 9 (9 self)
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The main result of this note is that an open simply connected 3manifold W³ proper homotopically dominated by a weak geometrically simply connected polyhedron is simply connected at infinity. This generalizes the main result of [16].
ONERELATOR GROUPS AND PROPER 3REALIZABILITY
, 910
"... Abstract. How different is the universal cover of a given finite 2complex from a 3manifold (from the proper homotopy viewpoint)? Regarding this question, we recall that a finitely presented group G is said to be properly 3realizable if there exists a compact 2polyhedron K with π1(K) ∼ = G whos ..."
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Abstract. How different is the universal cover of a given finite 2complex from a 3manifold (from the proper homotopy viewpoint)? Regarding this question, we recall that a finitely presented group G is said to be properly 3realizable if there exists a compact 2polyhedron K with π1(K) ∼ = G whose universal cover ˜K has the proper homotopy type of a PL 3manifold (with boundary). In this paper, we study the asymptotic behavior of finitely generated onerelator groups and show that those having finitely many ends are properly 3realizable, by describing what the fundamental progroup looks like, showing a property of onerelator groups which is stronger than the QSF property of Brick (from the proper homotopy viewpoint) and giving an alternative proof of the fact that onerelator groups are semistable at infinity. 1.
unknown title
, 2008
"... Noncompact 3manifolds proper homotopy equivalent to geometrically simply connected polyhedra and proper 3realizability of groups ..."
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Noncompact 3manifolds proper homotopy equivalent to geometrically simply connected polyhedra and proper 3realizability of groups
unknown title
, 2008
"... Noncompact 3manifolds proper homotopy equivalent to geometrically simply connected polyhedra and proper 3realizability of groups ..."
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Noncompact 3manifolds proper homotopy equivalent to geometrically simply connected polyhedra and proper 3realizability of groups
Groups which are not properly 3realizable
, 2009
"... A group is properly 3realizable if it is the fundamental group of a compact polyhedron whose universal covering is proper homotopically equivalent to some 3manifold. We prove that when such a group is also quasisimply filtered then it has pro(finitely generated free) fundamental group at infinit ..."
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A group is properly 3realizable if it is the fundamental group of a compact polyhedron whose universal covering is proper homotopically equivalent to some 3manifold. We prove that when such a group is also quasisimply filtered then it has pro(finitely generated free) fundamental group at infinity and semistable ends. Conjecturally the quasisimply filtration assumption is superfluous. Using these restrictions we provide the first examples of finitely presented groups which are not properly 3realizable, for instance large families of Coxeter groups.
Appendix: A Dehn exhaustibility Lemma
"... The main result of this note is that a special polyhedron which is proper homotopy equivalent to a geometrically simply connected polyhedron is Dehn exhaustible. AMS MOS Subj.Classification(1991): 57 M 50, 57 M 10, 57 M 30. Keywords and phrases: Proper homotopy, geometric simple connectivity, simp ..."
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The main result of this note is that a special polyhedron which is proper homotopy equivalent to a geometrically simply connected polyhedron is Dehn exhaustible. AMS MOS Subj.Classification(1991): 57 M 50, 57 M 10, 57 M 30. Keywords and phrases: Proper homotopy, geometric simple connectivity, simple connectivity at infinity, \Phi=\Psitheory. 1 Introduction Definition 1.1 The simplyconnected noncompact space W is Dehn exhaustible if, for any compact K ae W there exists some simply connected compact space L and a commutative diagram K f ! L i & # g W where i is the inclusion, i(K) ae int(L), f is an embedding, g is an immersion and f(K) " M 2 (g) = ;. Definition 1.2 The polyhedron W n of dimension n is a pseudomanifold if every point has a neighborhood homeomorphic to an open subset (with compact closure) of one of the following local models: 1. the Euclidean (half) space R n + , when it is called a regular point. 2. the open book made from p half nplanes having in com...
unknown title
, 2009
"... Noncompact 3manifolds proper homotopy equivalent to geometrically simply connected polyhedra and proper 3realizability of groups ..."
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Noncompact 3manifolds proper homotopy equivalent to geometrically simply connected polyhedra and proper 3realizability of groups