Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4243

 Title: Lifting Braids Authors: Mulazzani, MichelePiergallini, Riccardo Keywords: branched covering of the diskliftable homeomorphismliftable braid Issue Date: 2001 Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche Citation: Michele Mulazzani and Riccardo Piergallini, "Lifting Braids", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 32 (2001) suppl.1, pp. 193–219. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics32 suppl. 1 (2001) Abstract: In this paper we study the homeomorphisms of B$^{2}$ that are liftable with respect to a simple branched covering. Since any such homeomorphism maps the branch set of the covering onto itself and liftability is invariant up to isotopy fi{}xing the branch set, we are dealing in fact with liftable braids. We prove that the group of liftable braids is fi{}nitely generated by liftable powers of half-twists around arcs joining branch points. A set of such generators is explicitly determined for the special case of branched coverings B$^{2}$ $\rightarrow$ B$^{2}$ . As a preliminary result we also obtain the classifi{}cation of all the simple branched coverings of B$^{2}$. URI: http://hdl.handle.net/10077/4243 ISSN: 0049-4704 MS Classification: 57M12 Appears in Collections: Rendiconti dell‘ Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.32 (2001) s1

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