Coxeter Groups and Asphericalmanifolds
نویسنده
چکیده
I. Contractible manifolds and aspherical manifolds. Suppose that M n is a compact, contractible n-manifold with boundary. These assumptions imply that the boundary of M has the homology of an (n-l)-sphere; however, they do not imply that it is simply connected. If n ~ 3, then for M n to be homeomorphic to a disk it is obviously necessary that ~M be simply connected. For n ~ 5 this condition is also sufficient (cf. [5], [13], [18], [19]). On the other hand, for n ~ 4, there exist examples of such M n with non-simply cormected boundary (cf. Ill], [12], [14]). In fact, if n ~ 6, then the fundamental group of the boundary can be any group G satisfying HI(G) = 0 = H2(G) (cf. [9]). A non-compact space W is simply connected at ~ if every neighborhood of (i.e., every complement of a compact set) contains a simply connected neighborhood of ~. Suppose W is a locally compact, second countable, Hausdorff space with one end (i.e., it is connected at ~). Then W can be written as an increasing union of compact sets W =~=I Ci where CICC2 ~ C..., and where each W C i is connected. The space W is semi-stable if the inverse sequence
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تاریخ انتشار 2006