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Bordism theory and the Kervaire semi-characteristic

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Abstract

By using the bordism group, this paper provides an alternative proof of Weiping Zhangs’ theorem on counting Kervaire semi-characteristic.

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References

  1. Thomas, E., Vector fields on manifolds, Bull. Amer. Math. Soc., 1969, 75: 643–683.

    Article  MATH  MathSciNet  Google Scholar 

  2. Atiyah, M. F., Vector fields on manifolds, Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen, Heft 200, Düsseldorf, 1969.

  3. Koschorke, U., Vector fields and other vector bundle morphisms-a singularity approach, LNM Vol. 847, Berlin: Springer-Verlag, 1980.

    Google Scholar 

  4. Atiyah, M. F., Dupont, J., Vector fields with finite singularities, Acta Math., 1972, 128: 1–40.

    Article  MATH  MathSciNet  Google Scholar 

  5. Zhang, W., A counting formula for the Kervaire semi-characteristic, Topology, 2000, 39: 643–655.

    Article  MATH  MathSciNet  Google Scholar 

  6. Shubin, M., Novikov inequalities for vector fields, The Gelfand Math. Seminar, 1993–1995, Boston: Birkhäuser, 1996, 243–274.

    Google Scholar 

  7. Zhang, W., Analytic and topological invariants associated to nowhere zero vector fields, Pacific J. of Math., 1999, 187: 379–398.

    Article  MATH  Google Scholar 

  8. Witten, E., Supersymmetry and Morse theory, J. of Diff. Geom., 1982, 17: 661–692.

    MATH  MathSciNet  Google Scholar 

  9. Bismut, J. M., Lebeau, G., Complex immersions and Quillen metrics, Pub. Math. IHES, 1991, 74: 1–297.

    MATH  Google Scholar 

  10. Pontrjagin, L. S., Smooth manifolds and their applications to homotopy theory, Amer. Math. Soc. Translations, Ser. 2, Vol. 11, Providence: AMS, 1–114.

  11. Wall, C. T., Surgery on Compact Manifolds, London and New York: Academic Press, 1970.

    MATH  Google Scholar 

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Correspondence to Zizhou Tang.

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Tang, Z. Bordism theory and the Kervaire semi-characteristic. Sci. China Ser. A-Math. 45, 716–720 (2002). https://doi.org/10.1360/02ys9078

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  • DOI: https://doi.org/10.1360/02ys9078

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