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Geometrical realization of low-dimensional complete intersections

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Abstract

This paper aims to give some examples of diffeomorphic (or homeomorphic) low-dimensional complete intersections, which can be considered as a geometrical realization of classification theorems about complete intersections. A conjecture of Libgober and Wood (1982) will be confirmed by one of the examples.

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References

  1. Jupp, P., Classification of certain 6-manifolds, Proc. Cambridge Philos. Soc., 73, 1973, 293–300.

    Article  MathSciNet  MATH  Google Scholar 

  2. Wall, C. T. C., Classification problems in differential topology. On certain 6-manifolds, Invent. Math., 1, 1966, 355–374.

    Article  MathSciNet  MATH  Google Scholar 

  3. Freedman, M., The topology of four-dimensional manifolds, J. Differential Geom., 17, 1982, 357–453.

    MathSciNet  MATH  Google Scholar 

  4. Ebeling, W., An example of two homeomorphic, nondiffeomorphic complete intersection surfaces, Invent. Math., 99(3), 1990, 651–654.

    Article  MathSciNet  MATH  Google Scholar 

  5. Libgober, A. S. and Wood, J. W., Uniqueness of the complex structure on Kähler manifolds of certain homotopy types, J. Differential Geom., 32(1), 1990, 139–154.

    MathSciNet  MATH  Google Scholar 

  6. Fang, F. Q. and Klaus, S., Topological classification of 4-dimensional complete intersections, Manuscript Math., 90, 1996, 139–147.

    Article  MathSciNet  MATH  Google Scholar 

  7. Fang, F. Q. and Wang, J. B., Homeomorphism classification of complex projective complete intersections of dimensions 5, 6 and 7, Math. Z., 266, 2010, 719–746.

    Article  MathSciNet  MATH  Google Scholar 

  8. Kreck, M., Surgery and duality, Ann. of Math., 149(3), 1999, 707–754.

    Article  MathSciNet  MATH  Google Scholar 

  9. Traving, C., Klassification vollständiger Durchschnitte, Diplomarbeit, Mainz, 1985, http://www.info.de /Staff/traving.pdf

    Google Scholar 

  10. Brückmann, P., A remark on moduli spaces of complete intersections, J. Reine Angew. Math., 476, 1996, 209–215.

    MathSciNet  MATH  Google Scholar 

  11. Brückmann, P., A remark on moduli spaces of 4-dimensional complete intersections, J. Reine Angew. Math., 525, 2000, 213–217.

    MathSciNet  MATH  Google Scholar 

  12. Wang, J. B., Remarks on 5-dimensional complete intersections, Electron. Res. Announc. Math. Sci., 21, 2014, 28–40.

    MathSciNet  MATH  Google Scholar 

  13. Libgober, A. S. and Wood, J. W., Differentiable structures on complete intersections, I, Topology, 21, 1982, 469–482.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, China

    Jianbo Wang

  2. Graduate School, China Academy of Engineering Physics, Beijing, 100088, China

    Jianpeng Du

Authors
  1. Jianbo Wang
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  2. Jianpeng Du
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Corresponding author

Correspondence to Jianbo Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11001195), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry and Beiyang Elite Scholar Program of Tianjin University (No. 0903061016).

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Wang, J., Du, J. Geometrical realization of low-dimensional complete intersections. Chin. Ann. Math. Ser. B 37, 523–532 (2016). https://doi.org/10.1007/s11401-016-1022-0

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  • DOI: https://doi.org/10.1007/s11401-016-1022-0

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