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Abánades, Miguel Angel; Kucharz, Wojciech

Algebraic equivalence of real algebraic cycles. (English) Zbl 0932.14033

Ann. Inst. Fourier 49, No. 6, 1797-1804 (1999).
Summary: Given a compact nonsingular real algebraic variety we study the algebraic cohomology classes given by algebraic cycles algebraically equivalent to zero.

Cited in 3 Documents

MSC:

14P25 Topology of real algebraic varieties
14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
55N35 Other homology theories in algebraic topology

Keywords:

real algebraic variety; algebraic cycles algebraically equivalent to zero; algebraic cohomology
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\textit{M. A. Abánades} and \textit{W. Kucharz}, Ann. Inst. Fourier 49, No. 6, 1797--1804 (1999; Zbl 0932.14033)
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References:

[1] S. AKBULUT and H. KING, Topology of real algebraic sets, Mathematical Sciences Research Institute Publications, Springer, 1992. · Zbl 0808.14045
[2] S. AKBULUT and H. KING, Transcendental submanifolds of rn, Comm. Math. Helv., 68 (1993), 308-318. · Zbl 0806.57017
[3] E. BIERSTONE and P. MILMAN, Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant, Invent. Math., 128 (1997), 207-302. · Zbl 0896.14006
[4] J. BOCHNAK and W. KUCHARZ, Algebraic models of smooth manifolds, Invent. Math., 97 (1989), 585-611. · Zbl 0687.14023
[5] A. BOREL et A. HAEFLIGER, La classe d’homologie fondamentale d’un espace analytique, Bull. Soc. Math. France, 89 (1961), 461-513. · Zbl 0102.38502
[6] P.E. CONNER, Differentiable periodic maps, Lecture Notes in Math., Vol. 738, Berlin-Heidelberg-New York, Springer, 1979. · Zbl 0417.57019
[7] W. FULTON, Intersection theory, Ergebnisse der Math., Vol. 2, Berlin-Heidelberg-New York, Springer, 1984. · Zbl 0541.14005
[8] H. HIRONAKA, Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math., 79 (1964), 109-326. · Zbl 0122.38603
[9] S.T. HU, Homotopy theory, New York, Academic Press, 1959. · Zbl 0088.38803
[10] W. KUCHARZ, Algebraic equivalence and homology classes of real algebraic cycles, Math. Nachr., 180 (1996), 135-140. · Zbl 0877.14003
[11] J. MILNOR and J. STASHEFF, Characteristic classes, Ann. of Math. Studies, Vol. 76, Princeton Univ. Press, 1974. · Zbl 0298.57008
[12] R. THOM, Quelques propriétés globales de variétés différentiables, Comm. Math. Helv., 28 (1954), 17-86. · Zbl 0057.15502
[13] A. TOGNOLI, Su una congettura di Nash, Ann. Scuola Norm. Sup. Pisa, 27 (1973), 167-185.. · Zbl 0263.57011
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