132 research outputs found
Generalized Hantzsche-Wendt Flat Manifolds
We study the family of closed Riemannian n-manifolds with holonomy group
isomorphic to , which we call generalized Hantzsche-Wendt manifolds.
We prove results on their structures, compute some invariants, and find
relations between them, illustrated in graph connecting the family.Comment: 16 pages, 1 figure. Revista Matematica Iberoamericana. Vol. 21, no. 3
(2005). (to appear
Teichmüller theory and collapse of flat manifolds
We provide an algebraic description of the Teichmüller space and moduli space of flat metrics on a closed manifold or orbifold and study its boundary, which consists of (isometry classes of) flat orbifolds to which the original object may collapse. It is also shown that every closed flat orbifold can be obtained by collapsing closed flat manifolds, and the collapsed limits of closed flat 3-manifolds are classified
K-theory of noncommutative Bieberbach manifolds
We compute $K-theory of noncommutative Bieberbach manifolds, which quotients
of a three-dimensional noncommutative torus by a free action of a cyclic group
Z_N, N=2,3,4,6.Comment: 19 page
Crystallographic groups and flat manifolds from surface braid groups
Let be a compact surface without boundary, and . We analyse the
quotient group of the surface braid group
by the commutator subgroup of the pure braid group
. If is different from the -sphere , we prove
that is isomorphic rho , and that is a
crystallographic group if and only if is orientable. If is orientable,
we prove a number of results regarding the structure of
. We characterise the finite-order elements of this
group, and we determine the conjugacy classes of these elements. We also show
that there is a single conjugacy class of finite subgroups of
isomorphic either to or to certain Frobenius
groups. We prove that crystallographic groups whose image by the projection
is a Frobenius group are not Bieberbach
groups. Finally, we construct a family of Bieberbach subgroups
of of dimension and whose
holonomy group is the finite cyclic group of order , and if
is a flat manifold whose fundamental group is
, we prove that it is an orientable K\"ahler manifold that
admits Anosov diffeomorphisms
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