2014/06/10 by Lev Birbrair, Birbrair, Lev, Alexandre Fernandes +5 · 1 citation
Computer Science · Mathematics · #03C64 #14P15 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Dynamics and Fractals #math.AG #msc:03C64 #msc:14P15
paper · pdf · doi:10.48550/arxiv.1406.2559
13 pages, 2 figures, added Section 5 on Geometric realization of abstract pizzas
openalex publication_date 2014/06/10 · arxiv created 2014/07/10 · arxiv updated 2014/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study Lipschitz contact equivalence of continuous function germs in the plane definable in a polynomially bounded o-minimal structure, such as semialgebraic and subanalytic functions. We partition the germ of the plane at the origin into zones where the function has explicit asymptotic behavior. Such a partition is called a pizza. We show that each function germ admits a minimal pizza, unique up to combinatorial equivalence. We show then that two definable continuous function germs are definably Lipschitz contact equivalent if and only if their corresponding minimal pizzas are equivalent.