Topological and geometric properties of graph-manifolds
Geometric Topology
2007-05-23 v1 Differential Geometry
Abstract
This is an exposition of results on the existence problem of -injective immersed and embedded surfaces in graph-manifolds, and also of nonpositively curved metrics on graph-manifolds, obtained by different authors. The results are represented from a unified point of view based on the notion of compatible cohomological classes and some difference equation on the graph of a graph-manifold (BKN-equation). Criteria for seven different properties of graph-manifolds at three levels are given: at the level of compatible cohomological classes; at the level of solutions to the BKN-equation; in terms of spectral properties of operator invariants of a graph-manifold.
Keywords
Cite
@article{arxiv.math/0309192,
title = {Topological and geometric properties of graph-manifolds},
author = {S. Buyalo and P. Svetlov},
journal= {arXiv preprint arXiv:math/0309192},
year = {2007}
}
Comments
65 pages; a survey article. To appear in SPb Math. J