Lipschitz Geometry of Real Semialgebraic Surfaces

Autor:	Birbrair, Lev, Gabrielov, Andrei
Rok vydání:	2022
Předmět:	Mathematics - Metric Geometry Mathematics - Algebraic Geometry 51F30 14P10 03C64
Druh dokumentu:	Working Paper
Popis:	We present here basic results in Lipschitz Geometry of semialgebraic surface germs. Although bi-Lipschitz classification problem of surface germs with respect to the inner metric was solved long ago, classification with respect to the outer metric remains an open problem. We review recent results related to the outer and ambient bi-Lipschitz classification of surface germs. In particular, we explain why the outer Lipschitz classification is much harder than the inner classification, and why the ambient Lipschitz Geometry of surface germs is very different from their outer Lipschitz Geometry. In particular, we show that the ambient Lipschitz Geometry of surface germs includes all of the Knot Theory. Comment: 11 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.05511 Zobrazit plný text záznamu View this record from Arxiv