Closures of T-homogeneous braids are real algebraic

Abstract

A link in $S^3$ is called real algebraic if it is the link of an isolated singularity of a polynomial map from ${\mathbb{R}}^4$ to ${\mathbb{R}}^2$. It is known that every real algebraic link is fibered and it is conjectured that the converse is also true. We prove this conjecture for a large family of fibered links, which includes closures of T-homogeneous (and therefore also homogeneous) braids and braids that can be written as a product of the dual Garside element and a positive word in the Birman-Ko-Lee presentation. The proof offers a construction of the corresponding real polynomial maps, which can be written as semiholomorphic functions. We obtain information about their polynomial degrees.

35 pages, 12 figures

References in corpus (1)

• Links of singularities of inner non-degenerate mixed functions