Equivariant virtual Betti numbers

Goulwen Fichou[1]

  • [1] Université de Rennes 1 Institut Mathématiques de Rennes Campus de Beaulieu 35042 Rennes Cedex (France)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 1, page 1-27
  • ISSN: 0373-0956

Abstract

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We define a generalised Euler characteristic for arc-symmetric sets endowed with a group action. It coincides with the Poincaré series in equivariant homology for compact nonsingular sets, but is different in general. We put emphasis on the particular case of ℤ / 2 ℤ , and give an application to the study of the singularities of Nash function germs via an analog of the motivic zeta function of Denef and Loeser.

How to cite

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Fichou, Goulwen. "Equivariant virtual Betti numbers." Annales de l’institut Fourier 58.1 (2008): 1-27. <http://eudml.org/doc/10309>.

@article{Fichou2008,
abstract = {We define a generalised Euler characteristic for arc-symmetric sets endowed with a group action. It coincides with the Poincaré series in equivariant homology for compact nonsingular sets, but is different in general. We put emphasis on the particular case of $\mathbb\{Z\}/2\mathbb\{Z\}$, and give an application to the study of the singularities of Nash function germs via an analog of the motivic zeta function of Denef and Loeser.},
affiliation = {Université de Rennes 1 Institut Mathématiques de Rennes Campus de Beaulieu 35042 Rennes Cedex (France)},
author = {Fichou, Goulwen},
journal = {Annales de l’institut Fourier},
keywords = {equivariant homology; arc symmetric sets; motivic integration; Blow-Nash equivalence; blow-Nash equivalence},
language = {eng},
number = {1},
pages = {1-27},
publisher = {Association des Annales de l’institut Fourier},
title = {Equivariant virtual Betti numbers},
url = {http://eudml.org/doc/10309},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Fichou, Goulwen
TI - Equivariant virtual Betti numbers
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 1
SP - 1
EP - 27
AB - We define a generalised Euler characteristic for arc-symmetric sets endowed with a group action. It coincides with the Poincaré series in equivariant homology for compact nonsingular sets, but is different in general. We put emphasis on the particular case of $\mathbb{Z}/2\mathbb{Z}$, and give an application to the study of the singularities of Nash function germs via an analog of the motivic zeta function of Denef and Loeser.
LA - eng
KW - equivariant homology; arc symmetric sets; motivic integration; Blow-Nash equivalence; blow-Nash equivalence
UR - http://eudml.org/doc/10309
ER -

References

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  12. J. Huisman, Real quotient singularities and nonsingular real algebraic curves in the boundary of the moduli space, Compositio Math. 118 (1999), 43-60 Zbl0949.14017MR1705976
  13. S. Koike, A. Parusiński, Motivic-type invariants of blow-analytic equivalence, Ann. Inst. Fourier 53 (2003), 2061-2104 Zbl1062.14006MR2044168
  14. M. Kontsevich, Lecture at Orsay, (1995) 
  15. T.-C. Kuo, On classification of real singularities, Invent. Math. 82 (1985), 257-262 Zbl0587.32018MR809714
  16. K. Kurdyka, Ensembles semi-algébriques symétriques par arcs, Math. Ann. 282 (1988), 445-462 Zbl0686.14027MR967023
  17. C. McCrory, A. Parusiński, Virtual Betti numbers of real algebraic varieties, C. R. Acad. Sci. Paris 336 (2003), 763-768 Zbl1073.14071MR1989277
  18. J. Van Hamel, Algebraic cycles and topology of real algebraic varieties, (1997), CWI Tract 129, Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam Zbl0986.14042MR1824786

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