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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Gluing copies of a 3-dimensional polyhedron to obtain a closed nonpositively curved pseudomanifold


Authors: D. Burago, S. Ferleger, B. Kleiner and A. Kononenko
Journal: Proc. Amer. Math. Soc. 129 (2001), 1493-1498
MSC (2000): Primary 51K10, 53C20; Secondary 52B10
Published electronically: January 8, 2001
MathSciNet review: 1707510
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Abstract | References | Similar Articles | Additional Information

Abstract:

Let $S$ be a smooth 3-dimensional nonpositively curved Riemannian manifold with corners, whose boundary consists of a finite number of geodesically convex nonpositively curved faces (for example, a Euclidean or hyperbolic polyhedron). We show that it is always possible to glue together finitely many copies of $S$ so as to get a nonpositively curved pseudomanifold without boundary.


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Additional Information

D. Burago
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
Email: burago@math.psu.edu

S. Ferleger
Affiliation: Renaissance Technology Corporation, 600 Rt. 25-A, East Setanket, New York 11787

B. Kleiner
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112-0090
Email: bkleiner@math.utah.edu

A. Kononenko
Affiliation: Renaissance Technology Corporation, 600 Rt. 25-A, East Setanket, New York 11787
Email: kononena@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05554-X
PII: S 0002-9939(01)05554-X
Received by editor(s): August 31, 1998
Published electronically: January 8, 2001
Additional Notes: The first author was partially supported by a Sloan Foundation Fellowship and NSF grant DMS-9803129. The second author was partially supported by a Sloan Dissertation Fellowship. The third author was supported by a Sloan Foundation Fellowship, and NSF grants DMS-95-05175, DMS-96-26911. The fourth author was supported by NSF grant DMS-9803092
Communicated by: Christopher Croke
Article copyright: © Copyright 2001 American Mathematical Society