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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
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Abstract | References | Similar Articles | Additional Information

Abstract: This is a unified exposition of results (obtained by different authors) on the existence of $\pi_1$-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

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