Aspherical relative presentations
نویسندگان
چکیده
منابع مشابه
Aspherical Manifolds, Relative Hyperbolicity, Simplicial Volume, and Assembly Maps
This paper contains examples of closed aspherical manifolds obtained as a by-product of recent work by the author [Bel] on the relative strict hyperbolization of polyhedra. The following is proved. (I) Any closed aspherical triangulated n-manifold M with hyperbolic fundamental group is a retract of a closed aspherical triangulated (n+ 1)manifold N with hyperbolic fundamental group. (II) If B1, ...
متن کاملAspherical Manifolds*
This is a survey on known results and open problems about closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are contractible. Many examples come from certain kinds of non-positive curvature conditions. The property aspherical, which is a purely homotopy theoretical condition, has many striking implications about the geometry and analysis of the manifold or ...
متن کاملOn the Asphericity of Length Four Relative Group Presentations
We investigate asphericity of the relative group presentation 〈G, t | atbtctdtet = 1〉 and prove it aspherical provided the subgroup of G generated by {ab−1, bc−1, cd−1, de−1} is neither finite cyclic nor a finite triangle group. We also prove a similar result for the closely related relative group presentation 〈G, s, t | αsβsγt = 1 = δtεtζs−1〉.
متن کاملUdc 512.543.7+512.543.16 Free Subgroups of One-relator Relative Presentations
Note that the existence of free subgroups in G̃ for n > 3 follows immediately from the free subgroup theorem for one-relator groups. Thus, Theorem 1 is nontrivial only for n = 2. The most difficult case is n = 1. An important role in this situation is played by the exponent sum of the generator in the relator. A word w = ∏ git εi ∈ G ∗ 〈t〉∞ is called unimodular if ∑ εi = 1. If the exponent sum o...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1992
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500005290