We define two kinds of invariants of links in closed 3-manifolds, the s-complexity (s ∈ ℕ) and the block number, by considering decompositions of links in closed orientable 3-manifolds by spines. The first one is a generalization of the complexity of links defined by Pervova and Petronio. After providing properties of these invariants, we construct special spines of strongly-cyclic coverings branched over generalized twist knots in lens spaces, including S 3 and ℝP 3, which provide upper bounds for the invariants.
ASJC Scopus subject areas
- Algebra and Number Theory