12 research outputs found
Bounded automorphisms and quasi-isometries of finitely generated groups
Let G be any finitely generated infinite group. Denote by K(G) the FC-centre
of G, i.e., the subgroup of all elements of G whose centralizers are of finite
index in G. Let QI(G) denote the group of quasi-isometries of G with respect to
word metric. We observe that the natural homomorphism from the group of
automorphisms of G to QI(G) is a monomorphism only if K(G) equals the centre
Z(G) of G. The converse holds if K(G)=Z(G) is torsion free. We apply this
criterion to many interesting classes of groups.Comment: This is the corrected version. Published in J. Group Theory, 8
(2005), 515--52
-triviality of low dimensional manifolds
A space is -trivial if for every real vector bundle over
the total Stiefel-Whitney class . It follows from a result of
Milnor that if is an orientable closed smooth manifold of dimension
or , then is not -trivial. In this note we completely characterize
-trivial orientable closed smooth manifolds in dimensions and . In
dimension , we describe necessary conditions for an orientable closed smooth
-manifold to be -trivial.Comment: 10 page