Double point self-intersection surfaces of immersions

Mohammad A. Asadi-Golmankhaneh; Peter J. Eccles

doi:10.2140/gt.2000.4.149

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arXiv · math/0003236

Double point self-intersection surfaces of immersions

Mohammad A. Asadi-Golmankhaneh·Peter J. Eccles

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Abstract

A self-transverse immersion of a smooth manifold M^{k+2} in R^{2k+2} has a double point self-intersection set which is the image of an immersion of a smooth surface, the double point self-intersection surface. We prove that this surface may have odd Euler characteristic if and only if k is congruent to 1 modulo 4 or k+1 is a power of 2. This corrects a previously published result by Andras Szucs. The method of proof is to evaluate the Stiefel-Whitney numbers of the double point self-intersection surface. By earier work of the authors these numbers can be read off from the Hurewicz image h(α) in H_{2k+2}Ω^{\infty }Σ^{\infty }MO(k) of the element αin π_{2k+2}Ω^{\infty }Σ^{\infty }MO(k) corresponding to the immersion under the Pontrjagin-Thom construction.

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BibTeX RIS

Mohammad A. Asadi-Golmankhaneh, Peter J. Eccles. 2000-03-11. Double point self-intersection surfaces of immersions. https://doi.org/10.2140/gt.2000.4.149

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