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On 4–fold covering moves

Nikos Apostolakis

Algebraic & Geometric Topology 3 (2003) 117–145

arXiv: math.GT/0302225

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 S3. 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 S3.

Keywords
branched covering, covering move, colored braid, colored link, $3$–manifold
Mathematical Subject Classification 2000
Primary: 57M12
Secondary: 57M25
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Publication
Received: 16 November 2002
Accepted: 7 February 2003
Published: 17 February 2003
Authors
Nikos Apostolakis
Department of Mathematics
University of California
Riverside CA 92521
USA