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 APM  Vol.2 No.3 , May 2012
Lattice of Finite Group Actions on Prism Manifolds
John E. Kalliongis, Ryo Ohashi
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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
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.
References

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[4]   J. Kalliongis and R. Ohashi, “Finite Group Actions on Prism Manifolds Which Preserve a Heegaard Klein Bot- tle,” Kobe Journal of Math, Vol. 28, No. 1, 2011, pp. 69- 89.

[5]   B. A. Davey and H. A. Priestley, “Introduction to Lattices and Order,” Cambridge Mathematical Textbooks, Cambridge University Press, Cambridge, 1990.

 
 
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