ON SELF-INTERSECTION INVARIANTS
Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 259-273

Voir la notice de l'article provenant de la source Cambridge University Press

We prove that the Hatcher–Quinn and Wall invariants of a self-transverse immersion f: Nn ↬ M2n 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: Nn ↬ M2n−1.
DOI : 10.1017/S0017089512000481
Mots-clés : Primary 57R42, 57R40, Secondary 57R19, 57R67
GRANT, MARK. ON SELF-INTERSECTION INVARIANTS. Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 259-273. doi: 10.1017/S0017089512000481
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[1] 1.Dax, J. P., Étude homotopique des espaces de plongements, Ann. Sci. École Norm. Super. 5 (4) (1972), 303–377. Google Scholar

[2] 2.Ekholm, T., Regular homotopy and Vassiliev invariants of generic immersions SkR 2k−1, k ≥ 4, J. Knot Theory Ramifications 7 (8) (1998), 1041–1064. Google Scholar | DOI

[3] 3.Haefliger, A., Plongements différentiables dans le domaine stable, Comment. Math. Helv. 37 (1962), 155–176. Google Scholar

[4] 4.Hatcher, A. and Quinn, F., Bordism invariants of intersections of submanifolds, Trans. Amer. Math. Soc. 200 (1974), 327–344. Google Scholar

[5] 5.Juhász, A., A geometric classification of immersions of 3-manifolds into 5-space, Manuscr. Math. 117 (1) (2005), 65–83. Google Scholar | DOI

[6] 6.Klein, J. R. and Williams, E. B., Homotopical intersection theory, I, Geom. Topol. 11 (2007), 939–977. Google Scholar | DOI

[7] 7.Klein, J. R. and Williams, E. B., Homotopical intersection theory, II: Equivariance, Math. Z. 264 (4) (2010), 849–880. Google Scholar

[8] 8.Koschorke, U., Vector fields and other vector bundle morphisms—A singularity approach, Lecture Notes in Mathematics, vol. 847 (Springer, Berlin, 1981). Google Scholar

[9] 9.Munson, B. A., A manifold calculus approach to link maps and the linking number, Algebr. Geom. Topol. 8 (4) (2008), 2323–2353. Google Scholar | DOI

[10] 10.Saeki, O., Szűcs, A. and Takase, M., Regular homotopy classes of immersions of 3-manifolds into 5-space, Manuscr. Math. 108 (1) (2002), 13–32. Google Scholar

[11] 11.Salikhov, K., Multiple points of immersions, preprint, arXiv:math/0203118 Google Scholar

[12] 12.Salomonsen, H. A., Bordism and geometric dimension, Math. Scand. 32 (1973), 87–111. Google Scholar | DOI

[13] 13.Shapiro, A., Obstructions to the imbedding of a complex in a euclidean space. I. The first obstruction, Ann. Math. 66 (2) (1957), 256–269. Google Scholar

[14] 14.Szűcs, A., Note on double points of immersions, Manuscr. Math. 76 (3–4) (1992), 251–256. Google Scholar | DOI

[15] 15.Wall, C. T. C., Surgery of non-simply-connected manifolds, Ann. Math. 84 (2) (1966), 217–276. Google Scholar

[16] 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] 17.Whitney, H., The self-intersections of a smooth n-manifold in 2n-space, Ann. Math. 45 (2) (1944), 220–246. Google Scholar

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