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Nonpositive sectional curvature for $ (p,q,r)$-complexes

Author: Daniel T. Wise
Journal: Proc. Amer. Math. Soc. 136 (2008), 41-48
MSC (2000): Primary 20F67
Published electronically: September 26, 2007
MathSciNet review: 2350386
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Abstract: We give a criterion for the nonpositive sectional curvature of $ (p,q,r)$-complexes. As a consequence, we show that certain $ 2$-complexes have locally indicable, coherent and even locally quasiconvex fundamental groups.

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

  • 1. Béla Bollobás.
    Extremal graph theory, volume 11 of London Mathematical Society Monographs.
    Academic Press Inc. [Harcourt Brace Jovanovich Publishers], London, 1978. MR 506522 (80a:05120)
  • 2. R. D. Dutton and R. C. Brigham.
    Edges in graphs with large girth.
    Graphs Combin., 7(4):315-321, 1991. MR 1143180 (93b:05075)
  • 3. David K. Garnick, Y. H. Harris Kwong, and Felix Lazebnik.
    Extremal graphs without three-cycles or four-cycles.
    J. Graph Theory, 17(5):633-645, 1993. MR 1242183 (94j:05068)
  • 4. J. P. McCammond and D. T. Wise.
    Coherence, local quasiconvexity, and the perimeter of 2-complexes.
    Geom. Funct. Anal., 15(4):859-927, 2005. MR 2221153
  • 5. Jonathan P. McCammond and Daniel T. Wise.
    Locally quasiconvex small-cancellation groups.
    Trans. Amer. Math. Soc.
    To Appear.
  • 6. D. T. Wise.
    Sectional curvature, compact cores, and local quasiconvexity.
    Geom. Funct. Anal., 14(2):433-468, 2004. MR 2062762 (2005i:53043)
  • 7. Daniel T. Wise.
    Coherence, local-indicability, and nonpositive immersions.
  • 8. Daniel T. Wise.
    On the vanishing of the 2nd $ L^2$ Betti number.

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Additional Information

Daniel T. Wise
Affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada

Keywords: Coherent groups, nonpositive sectional curvature
Received by editor(s): December 17, 2003
Received by editor(s) in revised form: September 8, 2006
Published electronically: September 26, 2007
Additional Notes: The author’s research was supported by grants from NSERC and FCAR
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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