Topological and geometric properties of graph-manifolds
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S. Buyalo and P. Svetlov
Translated by: the authors - St. Petersburg Math. J. 16 (2005), 297-340
- DOI: https://doi.org/10.1090/S1061-0022-05-00852-6
- Published electronically: March 9, 2005
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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.References
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Bibliographic 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
- 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).
- © Copyright 2005 American Mathematical Society
- Journal: St. Petersburg Math. J. 16 (2005), 297-340
- MSC (2000): Primary 57N10
- DOI: https://doi.org/10.1090/S1061-0022-05-00852-6
- MathSciNet review: 2068341