Geometry & Topology

Double point self-intersection surfaces of immersions

Mohammad A Asadi-Golmankhaneh and Peter J Eccles

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A self-transverse immersion of a smooth manifold Mk+2 in 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 k1 mod4 or k+1 is a power of 2. This corrects a previously published result by András Szűcs.

The method of proof is to evaluate the Stiefel–Whitney numbers of the double point self-intersection surface. By an earlier work of the authors, these numbers can be read off from the Hurewicz image h(α)H2k+2ΩΣMO(k) of the element απ2k+2ΩΣMO(k) corresponding to the immersion under the Pontrjagin–Thom construction.

Article information

Geom. Topol., Volume 4, Number 1 (2000), 149-170.

Received: 30 July 1999
Accepted: 29 February 2000
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R42: Immersions
Secondary: 55R40: Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20] 55Q25: Hopf invariants 57R75: O- and SO-cobordism

immersion Hurewicz homomorphism spherical class Hopf invariant Stiefel–Whitney number


Asadi-Golmankhaneh, Mohammad A; Eccles, Peter J. Double point self-intersection surfaces of immersions. Geom. Topol. 4 (2000), no. 1, 149--170. doi:10.2140/gt.2000.4.149.

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