On the multiple points of immersions in Euclidean spaces

Szűcs, András

doi:10.1090/S0002-9939-98-04361-5

On the multiple points of immersions in Euclidean spaces
HTML articles powered by AMS MathViewer

by András Szűcs PDF

Proc. Amer. Math. Soc. 126 (1998), 1873-1882 Request permission

Abstract:

Given a self-transverse immersion of a closed, oriented manifold in a euclidean space and a natural number $i$ we compute the oriented cobordism class of the manifold of $i$-tuple points.

References

Akhmetiev, P. - Rimányi, R. - Szűcs, A. A generalization of Banchoff’s theorem, To appear in Proc. Amer. Math. Soc.
M. F. Atiyah and F. Hirzebruch, Cohomologie-Operationen und charakteristische Klassen, Math. Z. 77 (1961), 149–187 (German). MR 156361, DOI 10.1007/BF01180171
Thomas F. Banchoff, Triple points and surgery of immersed surfaces, Proc. Amer. Math. Soc. 46 (1974), 407–413. MR 377897, DOI 10.1090/S0002-9939-1974-0377897-1
Peter John Eccles, Multiple points of codimension one immersions of oriented manifolds, Math. Proc. Cambridge Philos. Soc. 87 (1980), no. 2, 213–220. MR 553578, DOI 10.1017/S030500410005667X
Peter John Eccles, Codimension one immersions and the Kervaire invariant one problem, Math. Proc. Cambridge Philos. Soc. 90 (1981), no. 3, 483–493. MR 628831, DOI 10.1017/S0305004100058941
Peter J. Eccles, Double point manifolds of immersions of spheres in Euclidean space, Prospects in topology (Princeton, NJ, 1994) Ann. of Math. Stud., vol. 138, Princeton Univ. Press, Princeton, NJ, 1995, pp. 125–137. MR 1368656
J. Lannes, Sur les immersions de Boy, Algebraic topology, Aarhus 1982 (Aarhus, 1982) Lecture Notes in Math., vol. 1051, Springer, Berlin, 1984, pp. 263–270 (French). MR 764583, DOI 10.1007/BFb0075571
R. K. Lashof and S. Smale, Self-intersections of immersed manifolds, J. Math. Mech. 8 (1959), 143–157. MR 0101522, DOI 10.1512/iumj.1959.8.58010
Ralph J. Herbert, Multiple points of immersed manifolds, Mem. Amer. Math. Soc. 34 (1981), no. 250, xiv+60. MR 634340, DOI 10.1090/memo/0250
F. Hirzebruch, Topological methods in algebraic geometry, Third enlarged edition, Die Grundlehren der mathematischen Wissenschaften, Band 131, Springer-Verlag New York, Inc., New York, 1966. New appendix and translation from the second German edition by R. L. E. Schwarzenberger, with an additional section by A. Borel. MR 0202713
John W. Milnor and James D. Stasheff, Characteristic classes, Annals of Mathematics Studies, No. 76, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. MR 0440554
R. E. Stong, Manifolds which immerse in small codimension, Illinois J. Math. 27 (1983), no. 2, 182–223. MR 694640
Felice Ronga, On multiple points of smooth immersions, Comment. Math. Helv. 55 (1980), no. 4, 521–527. MR 604710, DOI 10.1007/BF02566703
András Szűcs, Double point surfaces of smooth immersions $M^n\to \textbf {R}^{2n-2}$, Math. Proc. Cambridge Philos. Soc. 113 (1993), no. 3, 601–613. MR 1207523, DOI 10.1017/S0305004100076234
András Szűcs, Cobordism of maps with simplest singularities, Topology Symposium, Siegen 1979 (Proc. Sympos., Univ. Siegen, Siegen, 1979), Lecture Notes in Math., vol. 788, Springer, Berlin, 1980, pp. 223–244. MR 585661
A. Szűcs, Cobordism groups of immersions of oriented manifolds, Acta Math. Hungar. 64 (1994), no. 2, 191–230. MR 1261497, DOI 10.1007/BF01874122
Robert Wells, Double covers and metastable immersions of spheres, Canadian J. Math. 26 (1974), 145–176. MR 339219, DOI 10.4153/CJM-1974-016-1