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The fundamental groups of algebraic varieties

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1474)

Keywords

  • Fundamental Group
  • Heisenberg Group
  • Massey Product
  • Hard Lefschetz Theorem
  • Compact Closed Manifold

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. D. ARAPURA ‘Hodge theory with local coefficients and fundamental groups of varieties’ Bull. Amer. Math. Soc. 20 (1989) 169–172.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. C. BENSON and C.S. GORDON ‘Kähler and symplectic structures on nilmanifolds’ Topology 27 (1988) 513–518.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. J.A. CARLSON and D. TOLEDO ‘Harmonic mappings of Kähler manifolds to locally symmetric spaces’ Publ. Math. I.H.E.S. (to appear).

    Google Scholar 

  4. P. DELIGNE, P. GRIFFITHS, J. MORGAN and D. SULLIVAN ‘Real homotopy theory of Kähler manifolds’ Invent. Math. 29 (1975) 245–274.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. W.M. GOLDMAN and J.J. MILLSON ‘The deformation theory of representations of fundamental groups of compact Kähler manifolds’ Publ. Math. I.H.E.S. 67 (1988) 43–96.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. P. GRIFFITHS and J. HARRIS ‘Principles of algebraic geometry’ Wiley, New York (1978).

    MATH  Google Scholar 

  7. P.A. GRIFFITHS and J.W. MORGAN ‘Rational homotopy theory and differential forms’ Birkäuser (1981).

    Google Scholar 

  8. M. GROMOV ‘Sur le groupe fondamental d'une variété kählérienne’ C.R. Acad. Sci. Paris 308 (1989) 67–70.

    MathSciNet  MATH  Google Scholar 

  9. H. HOPF ‘Zur topologie der komplexen mannigfaltigkeiten’ in 'studies and essays presented to R. Courant’ Interscience (1948) 167–185.

    Google Scholar 

  10. F.E.A. JOHNSON and E.G. REES On the fundamental group of a complex algebraic manifold' Bull. Lond. Math. Soc. 19 (1987) 463–466.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. K. KODAIRA ‘On the structure of compact complex analytic surfaces I’ Amer. J. Math 86 (1964) 751–798.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. J. MILNOR ‘Morse theory’ Annals of Math. Studies 51, Princeton Univ. Press (1963).

    Google Scholar 

  13. J.W. MORGAN ‘The algebraic topology of smooth algebraic varieties’ Pub. Math. I.H.E.S. 48(1978) 137–204.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. K. NOMIZU ‘On the cohomology of compact homogeneous spaces of nilpotent Lie groups’ Ann. of Math. 59 (1954) 531–538.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. J-P. SERRE 'sur la topologies des variétés algébriques en caractéristique p’ Symp. Int. de Topologia Algebraica, Mexico, UNESCO (1958) 24–53.

    Google Scholar 

  16. D. SULLIVAN ‘Infinitesimal computations in algebraic topology’ Publ. Math. I.H.E.S. 47 (1977) 269–331.

    CrossRef  MATH  Google Scholar 

  17. A. TOGNOLI ‘Algebraic approximation of manifolds and spaces’ Springer Lecture Notes in Math. 842 (1981) 73–94.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1991 Springer-Verlag

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Johnson, F.E.A., Rees, E.G. (1991). The fundamental groups of algebraic varieties. In: Jackowski, S., Oliver, B., Pawałowski, K. (eds) Algebraic Topology Poznań 1989. Lecture Notes in Mathematics, vol 1474. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084738

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  • DOI: https://doi.org/10.1007/BFb0084738

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54098-4

  • Online ISBN: 978-3-540-47403-6

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