Vector bundles over real algebraic surfaces and threefolds
Kucharz, Wojciech
Compositio Mathematica, Tome 60 (1986), p. 209-225 / Harvested from Numdam
Publié le : 1986-01-01
@article{CM_1986__60_2_209_0,
     author = {Kucharz, Wojciech},
     title = {Vector bundles over real algebraic surfaces and threefolds},
     journal = {Compositio Mathematica},
     volume = {60},
     year = {1986},
     pages = {209-225},
     mrnumber = {868138},
     zbl = {0615.14007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1986__60_2_209_0}
}
Kucharz, Wojciech. Vector bundles over real algebraic surfaces and threefolds. Compositio Mathematica, Tome 60 (1986) pp. 209-225. http://gdmltest.u-ga.fr/item/CM_1986__60_2_209_0/

[1] S. Akbulut and H. King: The topology of real algebraic sets with isolated singularities. Ann. of Math. (2) (1981) 425-446. | MR 621011 | Zbl 0494.57004

[2] H. Bass: Algebraic K-theory. Benjamin (1968). | MR 249491 | Zbl 0174.30302

[3] R. Benedetti and A. Tognoli: On real algebraic vector bundles. Bull. Sci. Math. (2) 104 (1980) 89-112. | MR 560747 | Zbl 0421.58001

[4] R. Benedetti and A. Tognoli: Remarks and counterexamples in the theory of real algebraic vector bundles and cycles. Lectures Notes in Math. 959 (1981) 198-211. | MR 683134 | Zbl 0498.14015

[5] J. Bochnak, W. Kucharz and M. Shiota: Divisor class groups of some rings of global real analytic, Nash or rational regular functions. Lecture Notes in Math. 959 (1981) 218-248. | MR 683136 | Zbl 0519.14019

[6] J. Bochnak, M. Coste and M.F. Roy: Géomètrie Algébrique Réelle (book in preparation). | Zbl 0633.14016

[7] J. Bochnak and W. Kucharz: On real algebraic morphisms into Sn, preprint.

[8] A. Borel and A. Haefliger: La classe d'homologie fondamentale d'une espace analytique. Bull. Soc. Math. France 89 (1961) 461-513. | Numdam | MR 149503 | Zbl 0102.38502

[9] R. Bott and L.W. Tu: Differential Forms in Algebraic Topology, GMT82, Springer-Verlag (1982). | MR 658304 | Zbl 0496.55001

[10] E.G. Evans Jr.: Projective modules as fibre bundles. Proc. Amer. Math. Soc. 27 (1971) 623-626. | MR 269642 | Zbl 0213.29801

[11] R. Fossum: Vector bundles over spheres are algebraic. Invent. Math. 8 (1969) 222-225. | MR 250298 | Zbl 0172.48502

[12] A.V. Geramita and L.G. Roberts: Algebraic vector bundles on projective spaces. Invent. Math. 10 (1970) 298-304. | MR 480519 | Zbl 0199.55601

[13] F. Hirzebruch: Topological methods in algebraic geometry. Springer-Verlag (1966). | MR 202713 | Zbl 0138.42001

[14] D. Husemoller: Fibre Bundles, second edition, Springer-Verlag (1975). | MR 370578 | Zbl 0307.55015

[15] J.P. Jouanolou: Comparson des K-theories algébrique et topologique de quelques varietes algébrique. C.R. Acad. Sc. Paris, Ser. A272 (1971) 1373-1375. | MR 292848 | Zbl 0227.14013

[16] M. Karoubi: K-theory. Springer-Verlag (1978). | Zbl 0382.55002

[17] W. Kucharz: On homology of real algebraic sets, Invent. Math. 82, 19-25 (1985). | MR 808106 | Zbl 0547.14018

[18] K. Lønsted: An algebrization of vector bundles on compact manifolds. Journal of Pure and Applied Algebra 2 (1972) 193-207. | Zbl 0236.55016

[19] N. Moore: Algebraic vector bundles over the 2-sphere. Invent. Math. 14 (1971) 167-172. | MR 294334 | Zbl 0224.14008

[20] J. Milnor, and J. Stasheff: Characteristic classes. Annals of Mathematics Studies 76, Princeton University Press (1974). | MR 440554 | Zbl 0298.57008

[21] M.P. Murthy: Vector bundles over affine surfaces birationally equivalent to a ruled surface. Ann. of Math. (2) (89) (1969) 242-253. | MR 241434 | Zbl 0185.24504

[22] J.J. Risler: Sur l'homologie des surface algébriques réelles. Lecture Notes in Math. 959 (1981) 381-385. | MR 683144 | Zbl 0503.14014

[23] L.G. Roberts: Comparison of algebraic and topological K-theory. Lecture Notes in Math. 342 (1973) 74-78. | MR 374139 | Zbl 0268.18014

[24] J.P. Serre: Faisceaux algébriques cohérents. Ann. of Math. 61 (1955) 197-278. | MR 68874 | Zbl 0067.16201

[25] R. Silhol: A bound on the order of H(a)n-1(X, Z/2) on a real algebraic variety. Lecture Notes in Math. 959 (1981) 443-450; | MR 683148 | Zbl 0558.14003

[26] M. Shiota: Real algebraic realization of characteristic classes. RIMS Kyoto University, 18 (2) (1982) 995-1008. | MR 688940 | Zbl 0518.14011

[27] E. Spanier: Algebraic Topology. McGraw-Hill Book Company: New York (1966). | MR 210112 | Zbl 0145.43303

[28] R.G. Swan: Vector bundles and projective modules. Trans. Amer. Math. Soc. 105 (1962) 264-277. | MR 143225 | Zbl 0109.41601

[29] A. Tognoli: Algebraic geometry and Nash functions. Inst. Math. Vol. III, Acad. Press London and New York (1978). | MR 556239 | Zbl 0418.14002