Abstract
We find a connection between the Rokhlin theorem on the signature of a four-dimensional manifold and the notion of a prem-mapping that arises from the theory of embeddings of smooth manifolds.
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References
A. Szucs, “On the cobordism groups of immersions and embeddings,”Math. Proc. Cambridge Philos. Soc.,109, 343–349 (1991).
A. Szucs, “Cobordism groups of immersions of oriented manifolds,”Acta. Math. Hungar.,64, No. 2, 191–230 (1994).
B. Morin and J. P. Petit, “Problématique du retournement de la sphère,”C. R. Acad. Sci. Paris,287, 767–770 (1978).
P. M. Akhmet'ev, “Smooth embeddings of low-dimensional manifolds,”Mat. Sb. [Math. USSR-Sb],185, No. 10, 3–26 (1994).
T. Banchoff, “Triple points and singularities of projections of immersed surfaces,”Proc. Amer. Math. Soc.,46, 402–406 (1974).
V. A. Rokhlin, “A proof of the Gudkov conjecture,”Funktsional. Anal. i Prilozhen. [Functional Anal. Appl.],6, No. 2, 62–64 (1972).
L. Guillou and A. Marin, editors,A la recherche de la Topologie perdue, Progress in Mathematics, Vol. 62, Birkhäuser, Basel (1986).
R. Kirby,The Topology of 4-Manifolds, Lecture Notes in Math., Vol. 1374, Springer-Verlag, New York-Berlin (1989).
R. Mandelbaum,Four-Dimensional Topology, University of Rochester (1981).
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Translated fromMatematicheskie Zametki, Vol. 59, No. 6, pp. 803–810, June, 1996.
I thank Prof. A. Szucs for informing me about the existence of a canonical orientationO on the double points curve of a prem-mapping of an oriented surface into ℝ3.
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Akhmet'ev, P.M. Prem-mappings, triple self-intersection points of oriented surfaces, and the Rokhlin signature theorem. Math Notes 59, 581–585 (1996). https://doi.org/10.1007/BF02307206
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DOI: https://doi.org/10.1007/BF02307206