Vector bundles over real algebraic surfaces and threefolds

Wojciech Kucharz

Compositio Mathematica (1986)

  • Volume: 60, Issue: 2, page 209-225
  • ISSN: 0010-437X

How to cite

top

Kucharz, Wojciech. "Vector bundles over real algebraic surfaces and threefolds." Compositio Mathematica 60.2 (1986): 209-225. <http://eudml.org/doc/89805>.

@article{Kucharz1986,
author = {Kucharz, Wojciech},
journal = {Compositio Mathematica},
keywords = {real algebraic set; characterize the topological vector bundles which are topologically isomorphic to strongly algebraic ones},
language = {eng},
number = {2},
pages = {209-225},
publisher = {Martinus Nijhoff Publishers},
title = {Vector bundles over real algebraic surfaces and threefolds},
url = {http://eudml.org/doc/89805},
volume = {60},
year = {1986},
}

TY - JOUR
AU - Kucharz, Wojciech
TI - Vector bundles over real algebraic surfaces and threefolds
JO - Compositio Mathematica
PY - 1986
PB - Martinus Nijhoff Publishers
VL - 60
IS - 2
SP - 209
EP - 225
LA - eng
KW - real algebraic set; characterize the topological vector bundles which are topologically isomorphic to strongly algebraic ones
UR - http://eudml.org/doc/89805
ER -

References

top
  1. [1] S. Akbulut and H. King: The topology of real algebraic sets with isolated singularities. Ann. of Math. (2) (1981) 425-446. Zbl0494.57004MR621011
  2. [2] H. Bass: Algebraic K-theory. Benjamin (1968). Zbl0174.30302MR249491
  3. [3] R. Benedetti and A. Tognoli: On real algebraic vector bundles. Bull. Sci. Math. (2) 104 (1980) 89-112. Zbl0421.58001MR560747
  4. [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. Zbl0498.14015MR683134
  5. [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. Zbl0519.14019MR683136
  6. [6] J. Bochnak, M. Coste and M.F. Roy: Géomètrie Algébrique Réelle (book in preparation). Zbl0633.14016
  7. [7] J. Bochnak and W. Kucharz: On real algebraic morphisms into Sn, preprint. Zbl0674.14013
  8. [8] A. Borel and A. Haefliger: La classe d'homologie fondamentale d'une espace analytique. Bull. Soc. Math. France89 (1961) 461-513. Zbl0102.38502MR149503
  9. [9] R. Bott and L.W. Tu: Differential Forms in Algebraic Topology, GMT82, Springer-Verlag (1982). Zbl0496.55001MR658304
  10. [10] E.G. Evans Jr.: Projective modules as fibre bundles. Proc. Amer. Math. Soc.27 (1971) 623-626. Zbl0213.29801MR269642
  11. [11] R. Fossum: Vector bundles over spheres are algebraic. Invent. Math.8 (1969) 222-225. Zbl0172.48502MR250298
  12. [12] A.V. Geramita and L.G. Roberts: Algebraic vector bundles on projective spaces. Invent. Math.10 (1970) 298-304. Zbl0199.55601MR480519
  13. [13] F. Hirzebruch: Topological methods in algebraic geometry. Springer-Verlag (1966). Zbl0138.42001MR202713
  14. [14] D. Husemoller: Fibre Bundles, second edition, Springer-Verlag (1975). Zbl0307.55015MR370578
  15. [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. Zbl0227.14013MR292848
  16. [16] M. Karoubi: K-theory. Springer-Verlag (1978). Zbl0382.55002
  17. [17] W. Kucharz: On homology of real algebraic sets, Invent. Math.82, 19-25 (1985). Zbl0547.14018MR808106
  18. [18] K. Lønsted: An algebrization of vector bundles on compact manifolds. Journal of Pure and Applied Algebra2 (1972) 193-207. Zbl0236.55016
  19. [19] N. Moore: Algebraic vector bundles over the 2-sphere. Invent. Math.14 (1971) 167-172. Zbl0224.14008MR294334
  20. [20] J. Milnor, and J. Stasheff: Characteristic classes. Annals of Mathematics Studies76, Princeton University Press (1974). Zbl0298.57008MR440554
  21. [21] M.P. Murthy: Vector bundles over affine surfaces birationally equivalent to a ruled surface. Ann. of Math. (2) (89) (1969) 242-253. Zbl0185.24504MR241434
  22. [22] J.J. Risler: Sur l'homologie des surface algébriques réelles. Lecture Notes in Math.959 (1981) 381-385. Zbl0503.14014MR683144
  23. [23] L.G. Roberts: Comparison of algebraic and topological K-theory. Lecture Notes in Math.342 (1973) 74-78. Zbl0268.18014MR374139
  24. [24] J.P. Serre: Faisceaux algébriques cohérents. Ann. of Math.61 (1955) 197-278. Zbl0067.16201MR68874
  25. [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; Zbl0558.14003MR683148
  26. [26] M. Shiota: Real algebraic realization of characteristic classes. RIMS Kyoto University, 18 (2) (1982) 995-1008. Zbl0518.14011MR688940
  27. [27] E. Spanier: Algebraic Topology. McGraw-Hill Book Company: New York (1966). Zbl0145.43303MR210112
  28. [28] R.G. Swan: Vector bundles and projective modules. Trans. Amer. Math. Soc.105 (1962) 264-277. Zbl0109.41601MR143225
  29. [29] A. Tognoli: Algebraic geometry and Nash functions. Inst. Math. Vol. III, Acad. PressLondon and New York (1978). Zbl0418.14002MR556239

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.