33 research outputs found
Kernel of the variation operator and periodicity of the open books
We consider a parallelizable -manifold which has the homotopy type of
the wedge product of -spheres and show that the group of pseudo-isotopy
classes of orientation preserving diffeomorphisms that keep the boundary
pointwise fixed and induce the trivial variation operator is a
central extension of the group of all homotopy -spheres by . Then we apply this result to study the periodicity
properties of branched cyclic covers of manifolds with simple open book
decompositions and extend the previous results of Durfee, Kauffman and Stevens
to dimensions 7 and 15.Comment: This is a revision and extension of the version which was accepted
for publication in "Topology and its Applications