Universal covers and 3-manifolds
نویسندگان
چکیده
منابع مشابه
Finite covers of random 3 - manifolds
A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficult question. In particular, we consider random Heegaard splittings by gluing t...
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It is shown in this paper that if a Haken 3-manifold contains an incompressible torus that is not boundary-parallel then either it has a finite cover that is a torus-bundle over the circle or it has finite covers with arbitrarily large first Betti number. In [He 4], Hempel conjectures that every Haken 3-manifold has a finite cover whose fundamental group has a nontrivial representation to the i...
متن کامل2 00 5 Finite Covers of Random 3 - Manifolds
A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficult question. In particular, we consider random Heegaard splittings by gluing t...
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The goal of this paper is to describe all closed, aspherical Riemannian manifolds M whose universal covers M̃ have have a nontrivial amount of symmetry. By this we mean that Isom(M̃) is not discrete. By the well-known theorem of Myers-Steenrod [MS], this condition is equivalent to [Isom(M̃) : π1(M)] = ∞. Also note that if any cover of M has a nondiscrete isometry group, then so does its universal ...
متن کامل2-torus Manifolds, Cobordism and Small Covers
Abstract. Let Mn be the set of equivariant unoriented cobordism classes of all ndimensional 2-torus manifolds, where an n-dimensional 2-torus manifold M is a smooth closed manifold of dimension n with effective smooth action of a rank n 2-torus group (Z2) . Then Mn forms an abelian group with respect to disjoint union. This paper determines the group structure of Mn and shows that each class of...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2000
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(99)00061-4