Topological and geometric properties of graph-manifolds

Authors:
S. Buyalo and P. Svetlov

Translated by:
the authors

Original publication:
Algebra i Analiz, tom **16** (2004), nomer 2.

Journal:
St. Petersburg Math. J. **16** (2005), 297-340

MSC (2000):
Primary 57N10

DOI:
https://doi.org/10.1090/S1061-0022-05-00852-6

Published electronically:
March 9, 2005

MathSciNet review:
2068341

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This is a unified exposition of results (obtained by different authors) on the existence of -injective immersed and embedded surfaces in graph-manifolds, and also of nonpositively curved metrics on graph-manifolds. The basis for unification is provided by the notion of compatible cohomology classes and by a certain difference equation on the graph of a graph-manifold (the BKN-equation). Criteria for seven different properties of graph-manifolds are given at three levels: at the level of compatible cohomology classes; at the level of solutions of the BKN-equation; and in terms of spectral properties of operator invariants of a graph-manifold.

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Additional Information

**S. Buyalo**

Affiliation:
St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia

Email:
sbuyalo@pdmi.ras.ru

**P. Svetlov**

Affiliation:
St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia

Email:
svetlov@pdmi.ras.ru

DOI:
https://doi.org/10.1090/S1061-0022-05-00852-6

Keywords:
Immersed and embedded surfaces,
compatible cohomology classes,
BNK-equation

Received by editor(s):
September 2, 2002

Published electronically:
March 9, 2005

Additional Notes:
Supported by CRDF (grant no. RM1-2381-ST-02) and by RFBR (grant no. 02-01-00090).

Article copyright:
© Copyright 2005
American Mathematical Society