On branched coverings of singular $(G,X)$-manifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866929339673608192 |
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| author | Brunswic, Léo |
| author_facet | Brunswic, Léo |
| contents | Branched covering have a long history from ramification of Riemann surfaces to realization of 3-manifolds as covering ramified over a knots; from geometrical topology to algebraic geometry. The present work investigates a notion of branched covering "à la Fox" which is particularly natural for (G,X)-manifolds. The work is two fold. First, we recall and enrich the current state of the art (based upon Montesinos) and develop a Galois theory for such branched covering together with a description of the fiber above branching points. As a consequence, we solve two open questions of Montesinos and construct an example related to another open question. Second, we present a theory of singular (G,X)-manifolds and apply the theory of branched covering we developped to extend the usual framework of (G,X)-manifolds to singular (G,X)-manifolds; in particular, we construct a developping map for such singular manifolds. An application to singular locally Minkowski manifolds is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_10610 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On branched coverings of singular $(G,X)$-manifolds Brunswic, Léo Geometric Topology Algebraic Topology 51H05 57M10 Branched covering have a long history from ramification of Riemann surfaces to realization of 3-manifolds as covering ramified over a knots; from geometrical topology to algebraic geometry. The present work investigates a notion of branched covering "à la Fox" which is particularly natural for (G,X)-manifolds. The work is two fold. First, we recall and enrich the current state of the art (based upon Montesinos) and develop a Galois theory for such branched covering together with a description of the fiber above branching points. As a consequence, we solve two open questions of Montesinos and construct an example related to another open question. Second, we present a theory of singular (G,X)-manifolds and apply the theory of branched covering we developped to extend the usual framework of (G,X)-manifolds to singular (G,X)-manifolds; in particular, we construct a developping map for such singular manifolds. An application to singular locally Minkowski manifolds is given. |
| title | On branched coverings of singular $(G,X)$-manifolds |
| topic | Geometric Topology Algebraic Topology 51H05 57M10 |
| url | https://arxiv.org/abs/2010.10610 |