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ON SELF-INTERSECTION INVARIANTS

Published online by Cambridge University Press:  02 August 2012

MARK GRANT
Affiliation:
School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom e-mail: Mark.Grant@nottingham.ac.uk
Corresponding
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Abstract

We prove that the Hatcher–Quinn and Wall invariants of a self-transverse immersion f: NnM2n coincide. That is, we construct an isomorphism between their target groups, which carries one onto the other. We also employ methods of normal bordism theory to investigate the Hatcher–Quinn invariant of an immersion f: NnM2n−1.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

1.Dax, J. P., Étude homotopique des espaces de plongements, Ann. Sci. École Norm. Super. 5 (4) (1972), 303377.CrossRefGoogle Scholar
2.Ekholm, T., Regular homotopy and Vassiliev invariants of generic immersions SkR 2k−1, k ≥ 4, J. Knot Theory Ramifications 7 (8) (1998), 10411064.CrossRefGoogle Scholar
3.Haefliger, A., Plongements différentiables dans le domaine stable, Comment. Math. Helv. 37 (1962), 155176.CrossRefGoogle Scholar
4.Hatcher, A. and Quinn, F., Bordism invariants of intersections of submanifolds, Trans. Amer. Math. Soc. 200 (1974), 327344.CrossRefGoogle Scholar
5.Juhász, A., A geometric classification of immersions of 3-manifolds into 5-space, Manuscr. Math. 117 (1) (2005), 6583.CrossRefGoogle Scholar
6.Klein, J. R. and Williams, E. B., Homotopical intersection theory, I, Geom. Topol. 11 (2007), 939977.CrossRefGoogle Scholar
7.Klein, J. R. and Williams, E. B., Homotopical intersection theory, II: Equivariance, Math. Z. 264 (4) (2010), 849880.CrossRefGoogle Scholar
8.Koschorke, U., Vector fields and other vector bundle morphisms—A singularity approach, Lecture Notes in Mathematics, vol. 847 (Springer, Berlin, 1981).CrossRefGoogle Scholar
9.Munson, B. A., A manifold calculus approach to link maps and the linking number, Algebr. Geom. Topol. 8 (4) (2008), 23232353.CrossRefGoogle Scholar
10.Saeki, O., Szűcs, A. and Takase, M., Regular homotopy classes of immersions of 3-manifolds into 5-space, Manuscr. Math. 108 (1) (2002), 1332.CrossRefGoogle Scholar
11.Salikhov, K., Multiple points of immersions, preprint, arXiv:math/0203118Google Scholar
12.Salomonsen, H. A., Bordism and geometric dimension, Math. Scand. 32 (1973), 87111.CrossRefGoogle Scholar
13.Shapiro, A., Obstructions to the imbedding of a complex in a euclidean space. I. The first obstruction, Ann. Math. 66 (2) (1957), 256269.CrossRefGoogle Scholar
14.Szűcs, A., Note on double points of immersions, Manuscr. Math. 76 (3–4) (1992), 251256.CrossRefGoogle Scholar
15.Wall, C. T. C., Surgery of non-simply-connected manifolds, Ann. Math. 84 (2) (1966), 217276.CrossRefGoogle Scholar
16.Wall, C. T. C., Surgery on compact manifolds (Ranicki, A. A., Editor), Mathematical Surveys and Monographs, vol. 69 (Amer. Math. Soc., Providence, RI, 1999).Google Scholar
17.Whitney, H., The self-intersections of a smooth n-manifold in 2n-space, Ann. Math. 45 (2) (1944), 220246.CrossRefGoogle Scholar

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