Lattice of Finite Group Actions on Prism Manifolds

John E. Kalliongis; Ryo Ohashi

doi:10.4236/apm.2012.23022

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Advances in Pure Mathematics > Vol.2 No.3, May 2012

Lattice of Finite Group Actions on Prism Manifolds ()

Department of Mathematics and Computer Science, Saint Louis University, St. Louis, USA.
Department of Mathematics, King’s College, Wilkes-Barre, USA.

DOI: 10.4236/apm.2012.23022 PDF HTML 3,986 Downloads 7,321 Views

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.

Keywords

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

Share and Cite:

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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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