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Equivariant classification of 2-torus manifolds

Zhi Lü, Mikiya Masuda (2009)

Colloquium Mathematicae

We consider locally standard 2-torus manifolds, which are a generalization of small covers of Davis and Januszkiewicz and study their equivariant classification. We formulate a necessary and sufficient condition for two locally standard 2-torus manifolds over the same orbit space to be equivariantly homeomorphic. This leads us to count the equivariant homeomorphism classes of locally standard 2-torus manifolds with the same orbit space.

Euler's Polyhedron Formula

Jesse Alama (2008)

Formalized Mathematics

Euler's polyhedron theorem states for a polyhedron p, thatV - E + F = 2,where V, E, and F are, respectively, the number of vertices, edges, and faces of p. The formula was first stated in print by Euler in 1758 [11]. The proof given here is based on Poincaré's linear algebraic proof, stated in [17] (with a corrected proof in [18]), as adapted by Imre Lakatos in the latter's Proofs and Refutations [15].As is well known, Euler's formula is not true for all polyhedra. The condition on polyhedra considered...

Facetas del politopo de recubrimiento con coeficientes en {0, 1, 2, 3}.

Miguel Sánchez García, M.ª Inés Sobrón Fernández, M.ª Candelaria Espinel Febles (1992)

Trabajos de Investigación Operativa

En dos artículos, publicados en 1989, Balas y Ng dan una metodología para construir facetas del politopo de recubrimiento con coeficientes en {0, 1, 2}. Siguiendo esta metodología, en el presente artículo decimos cómo se contruyen facetas de dicho politopo con coeficientes en {0, 1, 2, 3}.

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