Abstract
We give a formula to detect the oriented bordism class of a codimension one immersion of an oriented 7-manifold in terms of singularities of its singular Seifert surface, that is, a generic map from a compact 8-manifold which extends the given immersion. Our argument involves a study of a relative version of the Thom polynomials for certain singularities of generic maps from manifolds with non-empty boundaries.
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The author is partially supported by the Grant-in-Aid for Scientific Research (C), MEXT, Japan.
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Takase, M. Oriented bordism of codimension one immersions of 7-manifolds and relative Thom polynomials. Math. Z. 272, 101–108 (2012). https://doi.org/10.1007/s00209-011-0923-6
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DOI: https://doi.org/10.1007/s00209-011-0923-6
Keywords
- Immersion
- Cobordism
- 7-Manifold
- Relative Thom polynomial
- Singular Seifert surface
- Stable homotopy of spheres
- Singularity