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

Title: Lifting Braids
Authors: Mulazzani, Michele
Piergallini, Riccardo
Keywords: branched covering of the disk
liftable homeomorphism
liftable 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 Mathematics
32 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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