Lattice of Finite Group Actions on Prism Manifolds
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.
Cite this paper: J. Kalliongis and R. Ohashi, "Lattice of Finite Group Actions on Prism Manifolds," Advances in Pure Mathematics, Vol. 2 No. 3, 2012, pp. 149-168. doi: 10.4236/apm.2012.23022.
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