Skip to main content

Local Coefficients and the Herbert Formula


We discuss a generalization and applications of the Herbert formula for double points of immersions, when the normal bundle of the immersion admits an additional structure.

This is a preview of subscription content, access via your institution.


  1. 1.

    P. M. Akhmet’ev and P. J. Eccles, “The relationship between framed bordism and skew-framed bordism,” Bull. London Math. Soc., 39, No. 3, 473–481 (2007).

    MathSciNet  Article  Google Scholar 

  2. 2.

    P. Akhmetiev and O. Frolkina, “On non-immersibility of ℝP10 to ℝ15,” Topol. Its Appl., 160, No. 11, 1241–1254 (2013).

    Article  Google Scholar 

  3. 3.

    P. Akhmetiev and O. Frolkina, “On properties of skew-framed immersions cobordism groups,” Fundam. Prikl. Mat., 21, No. 5, 19–46 (2016).

    MathSciNet  Google Scholar 

  4. 4.

    P. J. Eccles, “Multiple points of codimension one immersions,” in: Topology Symposium, Siegen 1979, Lect. Notes Math., Vol. 788, Springer, Berlin (1980), pp. 23–38.

  5. 5.

    P. J. Eccles and M. Grant, “Bordism classes represented by multiple point manifolds of immersed manifolds,” Tr. Mat. Inst. Steklova, 252, 55–60 (2006).

    MathSciNet  MATH  Google Scholar 

  6. 6.

    M. Grant, Bordism of Immersions, Thesis (2006).

  7. 7.

    R. J. Herbert, Multiple Points of Immersed Manifolds, Mem. Amer. Math. Soc., Vol 250, Amer. Math. Soc., Providence (1981).

  8. 8.

    M. W. Hirsch, “Immersions of manifolds,” Trans. Am. Math. Soc., 93, 242–276 (1959).

    MathSciNet  Article  Google Scholar 

  9. 9.

    G. Lippner and A. Szűcs, “A new proof of the Herbert multiple-point formula,” J. Math Sci., 146, No. 1, 5523–5529 (2007).

  10. 10.

    L. S. Pontryagin. Smooth Manifolds and Their Applications to Homotopy Theory, Amer. Math. Soc. Transl., Ser. 2, Vol. 11, Amer. Math. Soc., Providence (1959).

  11. 11.

    A.Szűcs, “Cobordism of immersions and singular maps, loop spaces and multiple points,” Geometric Algebraic Topology, 18, 239–253 (1986).

  12. 12.

    R. Wells, “Cobordism groups of immersions,” Topology, 5 281–294 (1966).

    MathSciNet  Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to P. M. Akhmet’ev.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 21, No. 6, pp. 79–91, 2016.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Akhmet’ev, P.M., Popelenskii, T.Y. Local Coefficients and the Herbert Formula. J Math Sci 248, 719–727 (2020).

Download citation