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The link of the germ of a semi-algebraic metric space
Author(s):
Guillaume
Valette
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3083-3090.
MSC (2000):
Primary 14P10, 32B25, 154E40
Posted:
June 20, 2007
MathSciNet review:
2322737
Retrieve article in:
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Abstract:
In this paper we investigate the metric properties of semi-algebraic germs. More precisely we introduce a counterpart to the notion of link for semi-algebraic metric spaces, which is often used to study the topology. We prove that it totally determines the metric type of the germ. We give a nice consequence for semi-algebraically bi-Lipschitz homeomorphic semi-algebraic germs.
References:
-
- [B]
- L. Birbrair, Local bi-Lipschitz classification of
 -dimensional semialgebraic sets. Houston J. Math. 25 (1999), no. 3, 453-472. MR 1730886 (2000j:14091) - [BB1]
- L. Birbrair, J. P. Brasselet, Metric homology. Comm. Pure Appl. Math. 53 (2000), no. 11, 1434-1447. MR 1773415 (2001h:14075)
- [BB2]
- L. Birbrair, J. P. Brasselet, Metric homology for isolated conical singularities. Bull. Sci. Math. 126 (2002), no. 2, 87-95. MR 1906238 (2003d:14070)
- [BCR1]
- J. Bochnak, M. Coste, M-F. Roy, Géométrie Algébrique Réelle, Ergebnisse der Math. 12, Springer-Verlag (1987). MR 949442 (90b:14030)
- [BCR2]
- J. Bochnak, M. Coste, M-F. Roy, Real Algebraic Geometry, Ergebnisse der Math. 36, Springer-Verlag (1998). MR 1659509 (2000a:14067)
- [C]
- M. Coste, An introduction to O-minimal Geometry, Dip. Mat. Univ. Pisa, Dottorato di Ricerca in Matematica, Instituti Editoriali e Poligrafici Internazionali, Pisa (2000).
- [CK]
- M. Coste, K. Kurdyka, On the link of a stratum in a real algebraic set. Topology 31 (1992), no. 2, 323-336. MR 1167174 (93d:14088)
- [vDS]
- L. van den Dries, P. Speissegger. O-minimal preparation theorems. Model theory and applications, 87-116, Quad. Mat., 11, Aracne, Rome, 2002. MR 2159715 (2006m:03063)
- [M]
- T. Mostowski, Lipschitz equisingularity. Dissertationes Math. (Rozprawy Mat.) 243 (1985), 46 pp. MR 808226 (87e:32008)
- [S]
- M. Shiota, Geometry of subanalytic and semialgebraic sets. Progress in Mathematics, 150. Birkhäuser Boston, Inc., Boston, MA, 1997. MR 1463945 (99b:14061)
- [V1]
- G. Valette, Lipschitz triangulations. Illinois J. of Math., Vol. 49, No. 3, Fall 2005, 953-979. MR 2210270
- [V2]
- G. Valette, Hardt's theorem: A bi-Lipschitz version. C. R. Acad. Sci. Paris, Ser. I 340 (2005), issue 12, 895-900. MR 2152275 (2006a:14097)
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Additional Information:
Guillaume
Valette
Affiliation:
Instytut Matematyki, Uniwersytet Jagiellonski, ul. Reymonta 4, 30-059 Kraków, Poland
Email:
Guillaume.Valette@im.uj.edu.pl
DOI:
10.1090/S0002-9939-07-08878-8
PII:
S 0002-9939(07)08878-8
Received by editor(s):
September 23, 2005
Received by editor(s) in revised form:
July 14, 2006
Posted:
June 20, 2007
Additional Notes:
This paper was partially supported by the RAAG Network
Communicated by:
David Preiss
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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