On spatial theta-curves with the same -fold and -fold branched covering

Abstract

In this note, we study two types of spatial theta-curves having two -knotswhose each has two -knotsand a trivial knot or two trivial knots and a -bridge knot as constituent knots. Weshow that there is a -manifold such that is the -fold and -fold covering of branched over each type of spatial theta-curve. Furthermore, weinvestigate certain relations between the spatial theta-curves and between the closed -manifolds which are coverings of branched over them.