Cyclic branched covers of knots as links of real isolated singularities

Abstract

Given a real analytic function $f$ from ${\mathbb{R}}^4$ to ${\mathbb{R}}^2$ with isolated critical point at the origin, the link $L_f$ of the singularity is a real fibred knot in ${\mathbb{S}}^3$. From this singularities, we construct a family of real isolated suspension singularities from ${\mathbb{R}}^6$ to ${\mathbb{R}}^2$ such that its links are the total spaces of the $n$-branched cyclic coverings over the corresponding knots. In this way we obtain as links of singularities, $3$-manifolds that does not appear in the complex case, such as hyperbolic $3$-manifolds or the Hantzsche-Wendt manifold.

6 pages

References in corpus (1)

• New Open-book Decompositions in Singularity Theory