R. Charney and M. Davis, The Euler characteristic of a nonpositively curved, piecewise Euclidean manifold, Pacific J. Math. 171 (1995), 117--137.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are Coxeter complexes of nite Coxeter groups. Flag complexes are the same as clique complexes or stable set complexes of graphs. There is a lot of interest in obtaining information about f vectors of ag complexes. One of the most interesting open problems is known as the Charney Davis conjecture [27][87, p. 100] and is a discrete analogue of a conjecture of H. Hopf on the Euler characteristic of a closed Riemannian manifold of nonpositive sectional curvature. Charney and Davis made their conjecture originally for spherical ag complexes, but we have extended it to the Gorenstein case. ....

R. Charney and M. Davis, The Euler characteristic of a nonpositively curved, piecewise linear Euclidean manifold, Paci c J. Math. 171 (1995), 117-137. 29

....of the parts are as equal as possible. This conjecture would imply a far reaching conjecture by Eckho [36] and myself on face numbers of clique complexes and will have applications to the study of f vectors of nerves of boxes, 36, 37] It seems also related to a conjecture by Charney and Davis [25] on clique complexes which are spheres. See also [76] p. 103. 6.8 Are there more drastic forms of algebraic shifting A drastic shifting is a shifting operation which map every simplicial complex to an even more restricted class of complexes than the shifted complexes and still preserves some ....

R. Charney and M. Davis, The euler characteristic of a nonpositively curved, piecwise euclidean manifolds, Pacic J. Math. 171 (1995), 117{ 137.

....For an extension of h vector theory to this setting see [44] Gamma Charney and Davis considered simplicial complexes with no empty simplices of dimension greater than 1, and called them flag complexes. they made exciting conjectures concerning face numbers of flag polytopes and spheres. see [19]) Gamma Another class of polytopes which are of interest are polytopes with the property that every k face has at most Ck facets. 4.7. h vectors for more exotic structures As we saw h vectors and g vectors plays a crucial role in the study of polytopes and related combinatorial structures. It ....

R. Charney and M. Davis, The Euler characteristics of nonpositively curved, piecewise linear Euclidean manifolds, preprint.

....complex whose faces correspond to the complete subgraphs of G. Understanding the possible face numbers of such complexes is an important problem in extremal combinatorics related to Turan s theorem; see [49, 72] Suppose that K(G) is a triangulated sphere. What can be said then Charney and Davis [52] formulated a conjecture concerning the face numbers of such complexes which is closely related to conjectures of Hopf on the Euler characteristic of manifolds M with nonpositive sectional curvature. For some recent development, see [71] Cubical upper bound theorems Cubical complexes seem of ....

R. Charney and M. Davis, The Euler characteristic of a nonpositively curved, piecwise Euclidean manifolds, Pacic J. Math. 171 (1995), 117-137.

...., which reflect Poincar e duality for X Delta . Define the alternating sum oe(P ) d X i=0 ( Gamma1) i h i (P ) h(P; Gamma1) f(P; Gamma2) d X i=0 f i (P ) Gamma2) i ] a quantity which is (essentially) equivalent to one arising in a conjecture of Charney and Davis [6], related to a conjecture of Hopf (see Section 5 below) Note that when d is odd, oe(P ) vanishes by the Dehn Sommerville equations. When d is even, we have the following result (see Section 2) Theorem 1.1. Let P be a simple d dimensional polytope, with d even. Then oe(P ) is the signature of ....

....an obtuse, simple polytope, but this is false. For example, a regular 3 dimensional cube is non acute and simple, but no obtuse polytope can have the facial structure of a 3 cube. Remark 4.4. M. Davis has pointed out to us that the first assertion of Corollary 4. 2 can be proven using facts from [6] and the mirror construction M(P ) of the next section, without any assumption that P is rational. We defer a sketch of this proof until the description of M(P ) at the end of that section. Proof of Proposition 4.1. We begin by rephrasing some of our definitions about non acuteness and obtuseness ....

[Article contains additional citation context not shown here]

R. Charney and M. Davis, The Euler characteristic of a nonpositively curved, piecewise Euclidean manifold, Pacific J. Math., 171 (1995), 117--137.

....Coxeter complexes of finite Coxeter groups. Flag complexes are the same as clique complexes or stable set complexes of graphs. There is a lot of interest in obtaining information about f vectors of flag complexes. One of the most interesting open problems is known as the Charney Davis conjecture [23][82, p. 100] and is a discrete analogue of a conjecture of H. Hopf on the Euler characteristic of a closed Riemannian manifold of nonpositive sectional curvature. Charney and Davis made their conjecture originally for spherical flag complexes, but we have extended it to the Gorenstein case. ....

R. Charney and M. Davis, The Euler characteristic of a nonpositively curved, piecewise linear Euclidean manifold, Pacific J. Math. 171 (1995), 117--137.

No context found.

R. Charney and M. Davis, Euler characteristic of a nonpositively curved, piecewise Euclidean manifold. Pac. J. Math., 171 (1995), 117--137.

No context found.

R. Charney and M. Davis, Euler characteristic of a nonpositively curved, piecewise Euclidean manifold. Pac. J. Math., 171 (1995), 117--137.

No context found.

R. Charney and M. Davis, Euler characteristic of a nonpositively curved, piecewise Euclidean manifold. Pac. J. Math., 171 (1995), 117--137.

....of lattice paths from (0, 0) to (n, n) taking north or east steps which stay weakly above the diagonal y = x and have exactly k right turns [17, Problem 6.36] The Charney Davis quantity in this case can be evaluated using the second equality of Lemma 4. 1 specialized to a 1 = 2, a 2 = 1 (see also [10, 4]) Proposition 3.1. 0 for n even, Cm for n = 2m 1 odd. where Cm = m 1 2m is the Catalan number. For s = 3, Baxter permutations come into play. A permutation # = # 1 # n S n is called a Baxter permutation if for all 1 i j k l n the following two conditions are ....

R. Charney and M. Davis, Euler characteristic of a nonpositively curved, piecewise Euclidean manifold. Pac. J. Math., 171 (1995), 117--137.

No context found.

R. Charney and M. Davis, The Euler characteristic of a nonpositively curved, piecewise Euclidean manifold, Pacific J. Math. 171 (1995), 117--137.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC