ABSTRACT

Local Bilipschitz Classification of 2-dimensional semialgebraic sets

Mathematical Subject Classification 14P25

In the paper we present a combinatorial invariant for the problem of local bilipschitz classification of 2-dimensional semialgebraic or subanalytic sets so-called Hölder Complex. The invariant is complete in the following sense: two germs of 2-dimensional closed semialgebraic sets are bilipschitz equivalent if and only if the corresponding Hölder Complexes are combinatorially equivalent.