TL;DR
This paper introduces fuzzy orbifolds derived from the fuzzy sphere, including a commutative case mapped onto a lattice and non-commutative approximations of spaces with singularities, expanding the fuzzy space framework.
Contribution
It presents the first example of fuzzification of a space with singularities and generalizes the construction to other fuzzy spaces.
Findings
One fuzzy orbifold is exactly commutative and lattice-mappable.
Other fuzzy orbifolds approximate spaces with singularities.
The method can be extended to various fuzzy spaces.
Abstract
A family of fuzzy orbifolds are generated by looking at sub-algebras of the fuzzy sphere. One of them is actually commutative and can be mapped exactly onto a lattice. The others are fuzzy approximations of S^2/Z_N where Z_N is the cyclic group of rotations of angle 2pi/N and provides the first example of the ``fuzzification'' of a space with singularities (at the poles). This construction can easily be generalised to other fuzzy spaces.
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Taxonomy
TopicsFuzzy Logic and Control Systems · Fuzzy and Soft Set Theory · Rough Sets and Fuzzy Logic