109 research outputs found
Reconstructible graphs, simplicial flag complexes of homology manifolds and associated right-angled Coxeter groups
In this paper, we investigate a relation between finite graphs, simplicial
flag complexes and right-angled Coxeter groups, and we provide a class of
reconstructible finite graphs. We show that if is a finite graph which
is the 1-skeleton of some simplicial flag complex which is a homology
manifold of dimension , then the graph is reconstructible.Comment: 7 page
On splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature
In this paper, we show some splitting theorems for CAT(0) spaces on which a
product group acts geometrically and we obtain a splitting theorem for compact
geodesic spaces of non-positive curvature. A CAT(0) group is said to
be {\it rigid}, if determines the boundary up to homeomorphisms of a
CAT(0) space on which acts geometrically. C.Croke and B.Kleiner have
constructed a non-rigid CAT(0) group. As an application of the splitting
theorems for CAT(0) spaces, we obtain that if and are
rigid CAT(0) groups then so is .Comment: 14 page
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