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

Wise, Daniel

doi:10.1090/S0002-9939-07-08921-6

Nonpositive sectional curvature for $(p,q,r)$-complexes
HTML articles powered by AMS MathViewer

by Daniel T. Wise PDF

Proc. Amer. Math. Soc. 136 (2008), 41-48 Request permission

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

Béla Bollobás, Extremal graph theory, London Mathematical Society Monographs, vol. 11, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1978. MR 506522
R. D. Dutton and R. C. Brigham, Edges in graphs with large girth, Graphs Combin. 7 (1991), no. 4, 315–321. MR 1143180, DOI 10.1007/BF01787638
David K. Garnick, Y. H. Harris Kwong, and Felix Lazebnik, Extremal graphs without three-cycles or four-cycles, J. Graph Theory 17 (1993), no. 5, 633–645. MR 1242183, DOI 10.1002/jgt.3190170511
J. P. McCammond and D. T. Wise, Coherence, local quasiconvexity, and the perimeter of 2-complexes, Geom. Funct. Anal. 15 (2005), no. 4, 859–927. MR 2221153, DOI 10.1007/s00039-005-0525-8
Jonathan P. McCammond and Daniel T. Wise. Locally quasiconvex small-cancellation groups. Trans. Amer. Math. Soc. To Appear.
D. T. Wise, Sectional curvature, compact cores, and local quasiconvexity, Geom. Funct. Anal. 14 (2004), no. 2, 433–468. MR 2062762, DOI 10.1007/s00039-004-0463-x
Daniel T. Wise. Coherence, local-indicability, and nonpositive immersions. Preprint.
Daniel T. Wise. On the vanishing of the 2nd $L^2$ Betti number. Preprint.