Structure trees, networks and almost invariant sets
Combinatorics
2016-01-27 v1 Group Theory
Geometric Topology
Abstract
A self-contained account of the theory of structure trees for edge cuts in networks is given. Applications include a generalisation of the Max-Flow Min-Cut Theorem to infinite networks and a short proof of a conjecture of Kropholler. This gives a relative version of Stallings' Theorem on the structure of groups with more than one end. A generalisation of the Almost Stability Theorem is also obtained, which provides information about the structure of the Sageev cubing.
Cite
@article{arxiv.1601.06965,
title = {Structure trees, networks and almost invariant sets},
author = {M. J. Dunwoody},
journal= {arXiv preprint arXiv:1601.06965},
year = {2016}
}
Comments
28 pages, 7 figures. To appear in L.M.S Lecture Notes volume for Wolfgang Woess. arXiv admin note: text overlap with arXiv:1409.6872, arXiv:1311.3929