On 4-fold covering moves

Details On 4-fold covering moves On 4-fold covering moves

2003-02-19

arxiv.org/abs/math/0302225v2

Algebr. Geom. Topol. 3 (2003) 117-145

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-5.abs.html Version 2: corr

Scientific paper

We prove the existence of a finite set of moves sufficient to relate any two representations of the same 3-manifold as a 4-fold simple branched covering of S^3. We also prove a stabilization result: after adding a fifth trivial sheet two local moves suffice. These results are analogous to results of Piergallini in degree 3 and can be viewed as a second step in a program to establish similar results for arbitrary degree coverings of S^3.

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