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Lifting Braids
Mulazzani, Michele
Piergallini, Riccardo
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$^{2}$.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
32 suppl. 1 (2001)
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
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.
Languages
en
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