RT Journal Article
T1 Constructions of two-fold branched covering spaces
A1 Montesinos Amilibia, José María
A1 Whitten, Wilbur Carrington
AB By equivariantly pasting together exteriors of links in S3 that are invariant under several different involutions of S3, we construct closed orientable 3-manifolds that are two-fold branched covering spaces of S3 in distinct ways, that is, with different branch sets. Sufficient conditions are given to guarantee when the constructed manifold M admits an induced involution, h, and when M∕h≅S3. Using the theory of characteristic submanifolds for Haken manifolds with incompressible boundary components, we also prove that doubles, D(K,ρ), of prime knots that are not strongly invertible are characterized by their two-fold branched covering spaces, when ρ≠0. If, however, K is strongly invertible, then the manifold branch covers distinct knots. Finally, the authors characterize the type of a prime knot by the double covers of the doubled knots, D(K;ρ,η) and D(K∗;ρ,η), of K and its mirror image K∗ when ρ and η are fixed, with ρ≠0 and η ∈{−2,2}.
PB Pacific Journal of Mathematics
SN 0030-8730
YR 1986
FD 1986-12
LK https://hdl.handle.net/20.500.14352/64695
UL https://hdl.handle.net/20.500.14352/64695
LA eng
NO Comité Conjunto Hispano-Norteamericano
NO NSF
DS Docta Complutense
RD 7 abr 2025