English

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.

Keywords

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

R2 v1 2026-06-22T12:36:48.811Z