7 research outputs found
The lattice of periods of a group action and its topology
Cataloged from PDF version of article.In this thesis, we study the topology of the poset obtained by removing the
greatest and least elements of lattice of periods of a group action. For a G-set
X where G is a finite group, the lattice of periods is defined as the image of the
map from the subgroup lattice of G to the partition lattice of X which sends a
subgroup H of G to the partition of X whose blocks are the H-orbits of X. We
study the homotopy type of the associated simplicial complex. When the group
G belongs to one of the families dihedral group of order 2n
, dihedral group of
order 2p
n where p is an odd prime, semi-dihedral group, or quaternion group and
the set X is transitive, we find the homotopy type of the corresponding poset. If
G is the dihedral group of order 2n or one of semidihedral and quaternion groups,
we find that the homotopy type of the complex is either contractible or has the
homotopy type of three points. In the case of dihedral group of order 2p
n
, the
associated complex is either contractible or it has the homotopy type of p points
or it has the homotopy type of p + 1 points.Acan, HüseyinM.S