We extend the concept of orbifold to that of branchfold, in order to allow cone singularities with rational angles, and we show why branchfolds naturally fit in the theory of branched coverings. Then, we obtain a geometric goodness theorem for branchfolds and apply it to prove that a conifold can be endowed with a branchfold structure if and only if it has locally finite holonomy.
Branchfold and rational conifolds
S. Benvenuti
;R. Piergallini;
2011
Abstract
We extend the concept of orbifold to that of branchfold, in order to allow cone singularities with rational angles, and we show why branchfolds naturally fit in the theory of branched coverings. Then, we obtain a geometric goodness theorem for branchfolds and apply it to prove that a conifold can be endowed with a branchfold structure if and only if it has locally finite holonomy.File in questo prodotto:
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