Article citationsMore>>

J. Kalliongis and A. Miller, “Orientation Reversing Ac- tions on Lens Spaces and Gaussian Integers,” Journal of Pure and Applied Algebra, Vol. 212, No. 3, 2008, pp. 652-667. doi:10.1016/j.jpaa.2007.06.022

has been cited by the following article:

• TITLE: Lattice of Finite Group Actions on Prism Manifolds

  AUTHORS: John E. Kalliongis, Ryo Ohashi

  KEYWORDS: Finite Group Action; Prism 3-Manifold; Equivalence of Actions; Orbifold; Partially Ordered Set; Distributive Lattice

  JOURNAL NAME: Advances in Pure Mathematics, Vol.2 No.3, May 29, 2012

  ABSTRACT: The set of finite group actions (up to equivalence) which operate on a prism manifold M, preserve a Heegaard Klein bottle and have a fixed orbifold quotient type, form a partially ordered set. We describe the partial ordering of these actions by relating them to certain sets of ordered pairs of integers. There are seven possible orbifold quotient types, and for any fixed quotient type we show that the partially ordered set is isomorphic to a union of distributive lattices of a certain type. We give necessary and sufficent conditions, for these partially ordered sets to be isomorphic and to be a union of Boolean algebras.