Amalgamated Products and Properly 3-realizable Groups
نویسندگان
چکیده
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).
منابع مشابه
Ascending Hnn - Extensions and Properly 3 - Realisable Groups
The most useful constructions in Combinatorial Group Theory are amalgamated free products and HNN-extensions, and they are the two basic examples in the theory of graphs of groups due to Bass and Serre (see [9]). We recall that given a group G and a subgroup H 6 G together with monomorphisms (respectively homomorphisms) ψ, φ : H −→ G, the group determined by the presentation 〈 G, t; t−1ψ(h)t = ...
متن کاملFree Entropy Dimension in Amalgamated Free Products
We calculate the microstates free entropy dimension of natural generators in an amalgamated free product of certain von Neumann algebras, with amalgamation over a hyperfinite subalgebra. In particular, some ‘exotic’ Popa algebra generators of free group factors are shown to have the expected free entropy dimension. We also show that microstates and non–microstates free entropy dimension agree f...
متن کاملExactness of Reduced Amalgamated Free Product C {algebras
Some completely positive maps on reduced amalgamated free products of C∗–algebras are constructed, showing that every reduced amalgamated free product of exact C∗–algebras is exact. Consequently, every amalgamated free product of exact discrete groups is exact.
متن کاملOn bounded cohomology of amalgamated products of groups
We investigate the structure of the singular part of the second bounded cohomology group of amalgamated products of groups by constructing an analog of the initial segment of the Mayer-Vietoris exact cohomology sequence for the spaces of pseudocharacters.
متن کامل. G R ] 1 N ov 2 00 4 RELATIVE DEHN FUNCTIONS OF AMALGAMATED PRODUCTS AND HNN – EXTENSIONS
We obtain an upper bound for relative Dehn functions of amalgamated products and HNN–extensions with respect to certain collections of subgroups. Our main results generalize the combination theorems for relatively hyperbolic groups proved by Dahmani.
متن کامل