Metric theory of semialgebraic curves.

Lev Birbrair; Alexandre C. G. Fernandes

Revista Matemática Complutense (2000)

  • Volume: 13, Issue: 2, page 369-382
  • ISSN: 1139-1138

Abstract

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We present a complete bi-Lipschitz classification of germs of semialgebraic curves (semialgebraic sets of the dimension one). For this purpose we introduce the so-called Hölder Semicomplex, a bi-Lipschitz invariant. Hölder Semicomplex is the collection of all first exponents of Newton-Puiseux expansions, for all pairs of branches of a curve. We prove that two germs of curves are bi-Lipschitz equivalent if and only if the corresponding Hölder Semicomplexes are isomorphic. We also prove that any Hölder Semicomplex can be realized as a germ of some plane semialgebraic curve. Finally, we compare these Hölder Semicomplexes with Hölder Complexes-complete bi-Lipschitz invariant of two-dimensional semialgebraic sets.

How to cite

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Birbrair, Lev, and Fernandes, Alexandre C. G.. "Teoría métrica de curvas semialgebráicas.." Revista Matemática Complutense 13.2 (2000): 369-382. <http://eudml.org/doc/44492>.

@article{Birbrair2000,
author = {Birbrair, Lev, Fernandes, Alexandre C. G.},
journal = {Revista Matemática Complutense},
keywords = {Curvas algebraicas; Subálgebras; Subespacio invariante; Espacios de Holder generalizados; Métrica; Gérmenes de funciones; singularity; Newton-Puiseux expansion; bi-Lipschitz classification; germs of semialgebraic curves; Hölder semicomplex},
language = {spa},
number = {2},
pages = {369-382},
title = {Teoría métrica de curvas semialgebráicas.},
url = {http://eudml.org/doc/44492},
volume = {13},
year = {2000},
}

TY - JOUR
AU - Birbrair, Lev
AU - Fernandes, Alexandre C. G.
TI - Teoría métrica de curvas semialgebráicas.
JO - Revista Matemática Complutense
PY - 2000
VL - 13
IS - 2
SP - 369
EP - 382
LA - spa
KW - Curvas algebraicas; Subálgebras; Subespacio invariante; Espacios de Holder generalizados; Métrica; Gérmenes de funciones; singularity; Newton-Puiseux expansion; bi-Lipschitz classification; germs of semialgebraic curves; Hölder semicomplex
UR - http://eudml.org/doc/44492
ER -

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