Covering moves and Kirby calculus

dc.creatorBobtcheva, Ivelina
dc.creatorPiergallini, Riccardo
dc.date2004-07-02
dc.date2007-01-02
dc.date.accessioned2026-07-07T07:37:45Z
dc.date.available2026-07-07T07:37:45Z
dc.descriptionWe 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.descriptionMinor 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.identifierhttps://arxiv.org/abs/math/0407032
dc.identifierhttp://arxiv.org/abs/math/0407032
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120881
dc.subjectGeometric Topology
dc.subject57M12; 57M25; 57N10; 57N13; 57Q45
dc.titleCovering moves and Kirby calculus
dc.typetext

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