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Showing 1 to 5 of 5 for “"homotopy group"”.
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Cubical small-cancellation theory and large-dimensional hyperbolic groups
Given a finitely presented group Q and a compact special cube complex X with nonelementary hyperbolic fundamental group, we produce a non-elementary, torsion-free, cocompactly cubulated hyperbolic group Γ that surjects onto Q, with kernel isomorphic to a quotient of G = π_1X and such that …
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Homotopy Theory of Monoids and Group Completion
… several complete and partial models for the homotopy theory of monoids and the derived functor of group completion. We show that there is a simplicial model structure on the category of reduced simplicial sets that is Quillen equivalent to the Quillen model structure of simplicial monoids. …
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Homotopy mapping spaces
<p>In algebraic topology, one studies the group structure of sets of homotopy classes of maps (such as the homotopy groups pin( X)) to obtain information about the spaces in question. It is also possible to place natural topologies on these groups that remember local properties ignored by the …
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Three-dimensional manifolds
… which it is proved that elements of the second homotopy group of a 3-manifold can be represented, in a certain sense, by 2-spheres or projective planes in the manifold. The Projective Plane Theorem is, perhaps, an important tool in the problem of classifying non-orientable 3-manifolds. The …
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Un ejemplo de teoría de homotopia en los grupos abelianos
… unitary ring R, we have developed a new homotopy theory in the category of abelian groups. The homotopy category of this theory has the following property: if an abelian group A admits the structrure of an R-module, then A has the homotopy type of the zero abelian group. As a consequence …