Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

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
Published electronically: March 9, 2005
MathSciNet review: 2068341
Full-text PDF Free Access

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 57N10

Retrieve articles in all journals with MSC (2000): 57N10


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: http://dx.doi.org/10.1090/S1061-0022-05-00852-6
PII: S 1061-0022(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