Geometry & Topology
- Geom. Topol.
- Volume 4, Number 1 (2000), 149-170.
Double point self-intersection surfaces of immersions
A self-transverse immersion of a smooth manifold in 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 or 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 of the element corresponding to the immersion under the Pontrjagin–Thom construction.
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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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. https://projecteuclid.org/euclid.gt/1513883281