Open Access
2000 Double point self-intersection surfaces of immersions
Mohammad A Asadi-Golmankhaneh, Peter J Eccles
Geom. Topol. 4(1): 149-170 (2000). DOI: 10.2140/gt.2000.4.149

Abstract

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.

Citation

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Mohammad A Asadi-Golmankhaneh. Peter J Eccles. "Double point self-intersection surfaces of immersions." Geom. Topol. 4 (1) 149 - 170, 2000. https://doi.org/10.2140/gt.2000.4.149

Information

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

zbMATH: 0941.57025
MathSciNet: MR1742556
Digital Object Identifier: 10.2140/gt.2000.4.149

Subjects:
Primary: 57R42
Secondary: 55Q25 , 55R40 , 57R75

Keywords: Hopf invariant , Hurewicz homomorphism , immersion , spherical class , Stiefel–Whitney number

Rights: Copyright © 2000 Mathematical Sciences Publishers

Vol.4 • No. 1 • 2000
MSP
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