On 4–fold covering moves

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

Mathematical Subject Classification 2000

Primary: 57M12

Secondary: 57M25

References

Forward citations

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

Volume 3, issue 1 (2003)

Nikos Apostolakis