Algebraic and Geometric Topology 3 (2003), paper no. 5, pages 117-145.

On 4-fold covering moves

Nikos Apostolakis

Abstract. 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.

Keywords. Branched covering, covering move, colored braid, colored link, 3-manifold

AMS subject classification. Primary: 57M12. Secondary: 57M25.

DOI: 10.2140/agt.2003.3.117

E-print: arXiv:math.GT/0302225

Submitted: 16 November 2002. Accepted: 7 February 2003. Published: 17 February 2003. Corrected: 20 January 2004 (see page 138).

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Nikos Apostolakis
Department of Mathematics, University of California
Riverside CA 92521, USA
Email: nea@math.ucr.edu

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