Real root conjecture fails for five- and higher-dimensional spheres

Discrete and Computational Geometry

Volumn 34, Issue 2, 2005, Pages 269-284

  Gal, Swiatoslaw R ^a  

^a UNIVERSITY OF WROC AW   (Poland)

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EID: 23944468024     PISSN: 01795376     EISSN: 14320444     Source Type: Journal    
DOI: 10.1007/s00454-005-1171-5     Document Type: Article

References (19)

1. [Ba] D. Barnette, A proof of the lower bound conjecture for convex polytopes, Pacific J. Math. 46 (1973), 349-354.
2. [Br] P. Brändén, Counterexamples to the Neggers-Stanley Conjecture, Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 155-158.
3. [BL] L. Billera and C. Lee, Sufficiency of McMullen's conditions for f-vectors of simplicial polytopes, Bull. Amer. Math. Soc. 2 (1980), 181-185.
4. [C] J. W. Cannon, Shrinking cell-like decompositions of manifolds. Codimension three, Ann. Math. 110 (1979), 83-112.
5. [CD] R. Charney and M. Davis, The Euler characteristic of a nonpositively curved, piecewise Euclidean manifold, Pacific J. Math. 171 (1995), 117-137.
6. 2-cohomology of Coxeter groups, arXiv:math.GT/0402377.
7. 2-homology of right-angled Coxeter Groups, Geom. Topol. 5 (2001), 7-74.
8. [E] R. D. Edwards, The topology of manifolds and cell-like maps, Proc. ICM Helsinki, 1978, pp. 111-127.
9. [F] M. H. Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17(3) (1982), 357-453.
10. [Ga] S. R. Gal, On normal subgroups of coxeter groups generated by standard parabolic subgroups, to appear in Geom. Dedicata.
11. [Gr] M. Gromov, Hyperbolic Groups, in Essays in Group Theory, S. G. Gersten, ed., pp. 75-263, MSRI Publ. 8, Springer-Verlag, Berlin, 1987.
12. [Kai] G. Kalai, Rigidity and the lower bound theorem, T., Invent. Math. 88(1) (1987), 125-151.
13. [Kar] K. Karu, The cd-index of fans and lattices, arXiv:math.AG/0410513.
14. [Kl] V. Klee, A combinatorial proof of Poincaré's duality theorem, Canad. J. Math. 16 (1964), 517-531.
15. [RW] V. Reiner and V. Welker, On the Charney-Davis and Neggers-Stanley Conjectures, J. Combin. Theory Ser. A 109(2) (2005), 247-280.
16. [Se] J. P. Serre, Cohomologie des groupes discrets, in Prospects in Mathematics, pp. 77-169, Annal of Mathematical Studies No. 70, Princeton University Press, Princeton, NJ, 1971.
17. [Sta1] R. Stanley, Combinatorics and Commutative Algebra, Birkhäuser, Boston, MA, 1996.
18. [Sta2] R. Stanley, Flag f-vectors and the cd-index, Math. Z. 216 (1994), 483-499.
19. [Ste] J. Stembridge, Counterexamples to the poset conjecture of Neggers, Stanley, and Stembridge, to appear in Trans. Amer. Math. Soc.