vix.ing · top · new · best · stats · spec

Surface singularities in R4: first steps towards Lipschitz knot theory

2019/12/04 by Birbrair, Lev, Gabrielov, Andrei
#14B05 #14P10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1912.02002

Abstract

A link of an isolated singularity of a two-dimensional semialgebraic surface in R4 is a knot (or a link) in S3. Thus the ambient Lipschitz classification of surface singularities in R4 can be interpreted as a bi-Lipschitz refinement of the topological classification of knots (or links) in S3. We show that, given a knot K in S3, there are infinitely many distinct ambient Lipschitz equivalence classes of outer metric Lipschitz equivalent singularities in R4 with the links topologically equivalent to K.

Related