Covering moves and Kirby calculus
| dc.creator | Bobtcheva, Ivelina | |
| dc.creator | Piergallini, Riccardo | |
| dc.date | 2004-07-02 | |
| dc.date | 2007-01-02 | |
| dc.date.accessioned | 2026-07-07T07:37:45Z | |
| dc.date.available | 2026-07-07T07:37:45Z | |
| dc.description | We show that simple coverings of B^4 branched over ribbon surfaces up to certain local ribbon moves bijectively represent orientable 4-dimensional 2-handlebodies up to handle sliding and addition/deletion of cancelling handles. As a consequence, we obtain an equivalence theorem for simple coverings of S^3 branched over links, in terms of local moves. This result generalizes to coverings of any degree results by the second author and Apostolakis, concerning respectively the case of degree 3 and 4. We also provide an extension of our equivalence theorem to possibly non-simple coverings of S^3 branched over embedded graphs. This work represents the first part of our study of 4-dimensional 2-handlebodies. In the second part (arXiv:math.GT/0612806), we factor such bijective correspondence between simple coverings of B^4 branched over ribbon surfaces and orientable 4-dimensional 2-handlebodies through a map onto the closed morphisms in a universal braided category freely generated by a Hopf algebra object. | |
| dc.description | Minor corrections. Added reference to the second part of our study of 4-dimensional 2-handlebodies (arXiv:math.GT/0612806). 68 pages, 87 postscript figures, 42 references. LaTeX 2.09 file. Uses: geom.sty epsf.sty | |
| dc.identifier | https://arxiv.org/abs/math/0407032 | |
| dc.identifier | http://arxiv.org/abs/math/0407032 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120881 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M12; 57M25; 57N10; 57N13; 57Q45 | |
| dc.title | Covering moves and Kirby calculus | |
| dc.type | text |