منابع مشابه
Peripheral Splittings of Groups
We define the notion of a “peripheral splitting” of a group. This is essentially a representation of the group as the fundamental group of a bipartite graph of groups, where all the vertex groups of one colour are held fixed—the “peripheral subgroups”. We develop the theory of such splittings and prove an accessibility result. The theory mainly applies to relatively hyperbolic groups with conne...
متن کاملSplittings of Groups and Intersection Numbers
We prove algebraic analogues of the facts that a curve on a surface with self-intersection number zero is homotopic to a cover of a simple closed curve, and that two simple closed curves on a surface with intersection number zero can be isotoped to be disjoint. In [15] and [16], analogues of the classical JSJ-decompositions of Haken manifolds were described using the notion of isotopic disjoint...
متن کاملMapping Class Groups of Heegaard Splittings
The mapping class group of a Heegaard splitting is the group of connected components in the set of automorphisms of the ambient manifold that map the Heegaard surface onto itself. We find examples of elements of the mapping class group that are periodic, reducible and pseudo Anosov on the Heegaard surface, but are isotopy trivial in the ambient manifold. We prove structural theorems about the f...
متن کاملSplittings of generalized Baumslag–Solitar groups
We study the structure of generalized Baumslag–Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of smallest complexity (fully reduced decompositions) and give a simplified proof of the existence of deformations. We also prove a finiteness theorem and solve the...
متن کاملCanonical splittings of groups and 3-manifolds
We introduce the notion of a ‘canonical’ splitting over Z or Z × Z for a finitely generated group G. We show that when G happens to be the fundamental group of an orientable Haken manifold M with incompressible boundary, then the decomposition of the group naturally obtained from canonical splittings is closely related to the one given by the standard JSJ-decomposition of M . This leads to a ne...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1983
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1983.107.141