Geodesic
On 4–fold covering moves
Apostolakis, Nikos1
1Department of Mathematics, University of California, Riverside CA 92521, USA
Algebraic and Geometric Topology, Tome 3 (2003) no. 1, pp. 117-145
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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.

DOI : 10.2140/agt.2003.3.117
Keywords: branched covering, covering move, colored braid, colored link, $3$–manifold

Apostolakis, Nikos  1

1 Department of Mathematics, University of California, Riverside CA 92521, USA 
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Apostolakis, Nikos. On 4–fold covering moves. Algebraic and Geometric Topology, Tome 3 (2003) no. 1, pp. 117-145. doi: 10.2140/agt.2003.3.117

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[9] R Piergallini, Four-manifolds as 4–fold branched covers of $S^4$, Topology 34 (1995) 497

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