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Vanishing conditions for the simplicial volume
of compact complex varieties
Author:
Marina Ville
Journal:
Proc. Amer. Math. Soc. 124 (1996), 987-993
MSC (1991):
Primary 14C20, 14D05, 14F35, 14F45, 20F32, 32S50, 55N35
MathSciNet review:
1246538
Full-text PDF Free Access
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Additional Information
Abstract: Gromov has defined a notion of simplicial volume: it is a topological invariant for compact manifolds which is closely related to the fundamental group. We investigate here the relevance of this notion in the realm of complex varieties.
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Daniel
Barlet, Espace analytique réduit des cycles analytiques
complexes compacts d’un espace analytique complexe de dimension
finie, Fonctions de plusieurs variables complexes, II (Sém.
François Norguet, 1974–1975), Springer, Berlin, 1975,
pp. 1–158. Lecture Notes in Math., Vol. 482 (French). MR 0399503
(53 #3347)
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Frederick
P. Greenleaf, Invariant means on topological groups and their
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Reinhold Co., New York, 1969. MR 0251549
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Michael
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Witold
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4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
(3,312b)
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Lojasiewicz, Triangulation of semi-analytic sets, Ann. Scuola
Norm. Sup. Pisa (3) 18 (1964), 449–474. MR 0173265
(30 #3478)
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- D. Barlet, Espace analytique réduit des cycles analytiques complexes compacts d'un espace analytique complexe de dimension finie, Fonctions de Plusieurs Variables Complexes (Séminaire François Norguet 1974--75), Lecture Notes in Math., vol. 482, Springer-Verlag, Berlin and New York, 1975, pp. 1--158. MR 53:3347
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- F. Greenleaf, Invariant means on topological groups, Van Nostrand & Reinhold, Princeton, NJ, 1969. MR 40:4776
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- M. Goretsky and R. MacPherson, Stratified Morse Theory, Springer-Verlag, 1988.
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- M. Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. 56 (1982), 1--99. MR 84h:53053
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- W. Hurewicz and H. Wallman, Dimension theory, Princeton Univ. Press, Princeton, NJ, 1941. MR 3:312b
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- S. Lojasiewicz, Triangulation of semi-analytic sets, Ann. Scuola Norm. Sup. Pisa Ser. III 18 (1964), 449--474. MR 30:3478
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Additional Information
Marina Ville
Email:
ville@orphee.polytechnique.fr
DOI:
http://dx.doi.org/10.1090/S0002-9939-96-02652-4
PII:
S 0002-9939(96)02652-4
Keywords:
Simplicial volume,
complex variety,
fundamental group,
bounded cohomology
Received by editor(s):
July 31, 1992
Received by editor(s) in revised form:
September 30, 1993
Communicated by:
Peter Li
Article copyright:
© Copyright 1996 American Mathematical Society
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