Definitions for orbifold
orb·ifold

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1. orbifoldnoun

   A topological space in which every small enough neighborhood is homeomorphic to a quotient of real space by the action of a finite group.

2. Etymology: Named by William Thurston. From orbit and manifold.

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1. Orbifold

   In the mathematical disciplines of topology, geometry, and geometric group theory, an orbifold is a generalization of a manifold. It is a topological space with an orbifold structure. The underlying space locally looks like the quotient space of a Euclidean space under the linear action of a finite group. Definitions of orbifold have been given several times: by Satake in the context of automorphic forms in the 1950s under the name V-manifold; by Thurston in the context of the geometry of 3-manifolds in the 1970s when he coined the name orbifold, after a vote by his students; and by Haefliger in the 1980s in the context of Gromov's programme on CAT spaces under the name orbihedron. The definition of Thurston will be described here: it is the most widely used and is applicable in all cases. Mathematically, orbifolds arose first as surfaces with singular points long before they were formally defined. One of the first classical examples arose in the theory of modular forms with the action of the modular group SL on the upper half-plane: a version of the Riemann–Roch theorem holds after the quotient is compactified by the addition of two orbifold cusp points. In 3-manifold theory, the theory of Seifert fiber spaces, initiated by Seifert, can be phrased in terms of 2-dimensional orbifolds. In geometric group theory, post-Gromov, discrete groups have been studied in terms of the local curvature properties of orbihedra and their covering spaces.¹

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Numerology

1. Chaldean Numerology

   The numerical value of orbifold in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of orbifold in Pythagorean Numerology is: 9

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References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Orbifold
2. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=orbifold