2004/07/02 by Bobtcheva, Ivelina, Piergallini, Riccardo · 1 citation
#57M12 #57M25 #57N10 #57N13 #57Q45 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.math/0407032
We show that simple coverings of B4 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 S3 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 S3 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 B4 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.