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

Summary: Given a compact nonsingular real algebraic variety we study the algebraic cohomology classes given by algebraic cycles algebraically equivalent to zero.


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
Full Text: DOI Numdam EuDML


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.