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Double point surfaces of smooth immersions Mn → ℝ2n−2

Published online by Cambridge University Press:  24 October 2008

András Szücs
András Szücs
Affiliation:
Department of Analysis, Eötvös Loránd University, Budapest, Múzeum krt. 6–8, H-1088 Hungary
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Extract

In recent years many papers have dealt with the zero-dimensional multiple point sets of smooth immersions of closed manifolds in Euclidean spaces (see, for example, [2, 6, 7, 8, 9, 10, 13, 14, 15, 21]). In the present paper we deal with the case when the double points form a two-dimensional surface and consider the following question: Which surfaces can occur as double point surfaces of self-transverse immersions of closed n-manifolds in ℝ2n−2? We prove the following

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 3 , May 1993 , pp. 601 - 613
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

REFERENCES

[1]Adams, J. F.. Vector fields on spheres. Bull. Amer. Math. Soc. 68 (1962), 39–41.Google Scholar
[2]Banchoff, T.. Triple points and surgery of immersed surfaces. Proc. Amer. Math. Soc. 46, 407–413 (1974).CrossRefGoogle Scholar
[3]Brown, R.. Embeddings, immersions and cobordism of differentiable manifolds. Bull. Amer. Math. Soc. 76 (1970), 763–766.CrossRefGoogle Scholar
[4]Cohen, R. L.. The immersion conjecture for differentiable manifolds. Ann. of Math. (2) 122 (1985), 237–328.CrossRefGoogle Scholar
[5]Dold, A.. Erzeugende der Thomschen Algebra N*. Math. Z. 65 (1956), 25–35.CrossRefGoogle Scholar
[6]Eccles, P. J.. Multiple points of codimension one immersions. In Topology Symposium, Siegen 1979, Lecture Notes in Math. vol. 788 (Springer-Verlag, 1980), pp. 23–38.CrossRefGoogle Scholar
[7]Eccles, P. J.. Multiple points of codimension one immersions of oriented manifolds. Math. Proc. Cambridge Philos. Soc. 87 (1980), 213–220.CrossRefGoogle Scholar
[8]Eccles, P. J.. Codimension one immersions and the Kervaire invariant problem. Math. Proc. Cambridge Philos. Soc. 90 (1981), 483–493.CrossRefGoogle Scholar
[9]Eccles, P. J. and Mitchell, W. P. R.. Triple points of immersed orientable 2n-manifolds in 3n-space. J. London Math. Soc. (2) 39 (1989), 335–346.CrossRefGoogle Scholar
[10]Freedman, M.. Quadruple points of 3-manifolds in S 4. Comment. Math. Helv. 53 (1978), 385–394.CrossRefGoogle Scholar
[11]Haefliger, A.. Plongements differentiables de variétés dans variétés. Comment. Math. Helv. 36 (1962), 47–82.CrossRefGoogle Scholar
[12]Husemoller, D.. Fibre Bundles (McGraw-Hill Book Co., 1966).CrossRefGoogle Scholar
[13]Hughes, F.. Triple points of immersed 2n-manifolds in 3n-space. Quart. J. Math. Oxford Ser. (2) 34 (1983), 427–431.CrossRefGoogle Scholar
[14]Koschorke, U.. Multiple points of immersions and the Kahn–Priddy theorem. Math. Z. 169 (1979), 223–236.CrossRefGoogle Scholar
[15]Lannes, J.. Sur les immersions de Boy. In Algebraic Topology, Aarhus 1982, Lecture Notes in Math. vol. 1051 (Springer-Verlag, 1984), pp. 263–270.CrossRefGoogle Scholar
[16]Mahowald, M. E.. On obstruction theory in orientable fibre bundles. Trans. Amer. Math. Soc. 110 (1964), 315–349.CrossRefGoogle Scholar
[17]Mahowald, M. E. and Milgram, R. J.. Embedding real projective spaces. Ann. of Math. (2) 87 (1968), 411–422.CrossRefGoogle Scholar
[18]Rees, E.. Embeddings of real projective spaces. Topology 10 (1971), 309–312.Google Scholar
[19]Sanderson, B. J.. Immersions and embeddings of projective spaces. Proc. London Math. Soc. (3) 14 (1964), 137–153.CrossRefGoogle Scholar
[20]Szücs, A.. Cobordism of maps with simplest singularities. In Topology Symposium, Siegen 1979, Lecture Notes in Math. vol. 788 (Springer-Verlag, 1980), pp. 223–244.CrossRefGoogle Scholar
[21]Szücs, A.. On multiple points of odd multiplicity of immersions of odd codimensions. Bull. London Math. Soc. 22 (1990), 599–601.CrossRefGoogle Scholar
[22]Viro, O.. Some integral calculus based on Euler characteristic. In Topology and Geometry, Lecture Notes in Math. vol. 1346 (Springer-Verlag), pp. 127–138.Google Scholar
[23]Wall, C. T. C.. Determination of the cobordism ring. Ann. of Math. (2) 72 (1960), 292–311.Google Scholar
[24]Wells, R.. Double covers and metastable immersions of spheres. Canad. J. Math. 26 (1974), 145–176.CrossRefGoogle Scholar