منابع مشابه
Free crossed resolutions for graph products and amalgamated sums of groups
The category of crossed complexes gives an algebraic model of CW -complexes and cellular maps. We show how the strong properties of this category allow for the computation of free crossed resolutions of graph products of groups, and of free products with amalgamation, given free crossed resolutions of the individual groups. This gives computations of higher homotopical syzygies in these cases.
متن کاملCrossed Complexes, and Free Crossed Resolutions for Amalgamated Sums and Hnn-extensions of Groups
The category of crossed complexes gives an algebraic model of CW -complexes and cellular maps. Free crossed resolutions of groups contain information on a presentation of the group as well as higher homological information. We relate this to the problem of calculating non-abelian extensions. We show how the strong properties of this category allow for the computation of free crossed resolutions...
متن کاملAmalgamated Products and Properly 3-realizable Groups
In this paper, we show that the class of all properly 3-realizable groups is closed under amalgamated free products (and HNN-extensions) over finite groups. We recall that G is said to be properly 3-realizable if there exists a compact 2-polyhedron K with π1(K) = G and whose universal cover K̃ has the proper homotopy type of a 3-manifold (with boundary).
متن کاملHeegaard Stability in Amalgamated 3-manifolds I: Connected Sums
Let M1 and M2 be closed, irreducible 3-manifolds. Let Hi and Gi denote non-isotopic Heegaard surfaces in Mi, where Hi is unstabilized. Let H be the amalgamation of H1 and H2 and G be the amalgamation of G1 and G2 in M1#M2. Then H is not a stabilization of G. It follows that H and G are not isotopic, and that H is unstabilized. This answers a question of C. Gordon (Problem 3.91 from [Kir97]) in ...
متن کاملJ ul 2 00 2 Crossed complexes , and free crossed resolutions for amalgamated sums and HNN - extensions of groups ∗
The category of crossed complexes gives an algebraic model of CW-complexes and cellular maps. Free crossed resolutions of groups contain information on a presentation of the group as well as higher homological information. We relate this to the problem of calculating non-abelian extensions. We show how the strong properties of this category allow for the computation of free crossed resolutions ...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1996
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500023300