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On Generalized Homology of Artin Groups
Journal of Mathematical Sciences, 2003Generalized braid groups \(\text{Br}({\mathcal D}_\infty)\), \(\text{Br}({\mathcal C}_m)\) and \(\text{Br}^g_\infty\) (braids of an infinite number of strings in a genus \(g\) handlebody) are considered and the Morava \(K\)-theory \(K(n)_*(\text{Br}({\mathcal D}_\infty))\), \(K(n)_*(\text{Br}^g_\infty)\), the Brown-Peterson homology \(\text{BP}_*(\text{
Broto, C., Vershinin, V. V.
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Any relation between the elements of a set X and the elements of a set Y is associated with two simplicial complexes K and L. A simplex of K is a finite set of elements of X related to a common element of Y; a simplex of L is a finite set of elements of Y related to a common element of X.
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Character Group of a Relative Homology Group
The Annals of Mathematics, 1940If L is a subcomplex of a finite complex K, the topologically invariant factor group of the group of p-cycles of L bounding in K taken with respect to the subgroup of those bounding in L is useful in topology. The principal aim of this paper is to find its character group and to interpret the character group geometrically (theorems 4.2 and 4.4 at the ...
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Abelian Groups with a Vanishing Homology Group
Canadian Journal of Mathematics, 1969In this paper, we wish to characterize those abelian groups whose integral homology groups vanish in some positive dimension. We obtain a complete characterization provided the dimension in which the homology vanishes is odd; in fact, we prove that the only abelian groups which possess a vanishing homology group in an odd dimension are, up to ...
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