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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A generalization of Banchoff's
triple point theorem


Authors: P. Akhmetiev, R. Rimányi and A. Szucs
Journal: Proc. Amer. Math. Soc. 126 (1998), 913-915
MSC (1991): Primary 57R42
MathSciNet review: 1422840
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Abstract: Consider an immersion of a surface into $S^{3}$. Banchoff's theorem states that the parity of the number of triple points and the parity of the Euler characteristic of the surface coincide. Here we generalize this theorem to codimension 1 immersions of arbitrary even dimensional manifolds in spheres. The proof is an analogue of a proof of Banchoff's theorem circulated in preprint form due to R. Fenn and P. Taylor in 1977.


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Additional Information

P. Akhmetiev
Affiliation: Institute of Terrestrial Magnetism and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Moscow Region 142092, Russia

R. Rimányi
Affiliation: ELTE Department of Geometry, Budapest, Rákóczi út 5., 1088, Hungary

A. Szucs
Affiliation: ELTE Department of Analysis, Budapest, Múzeum krt. 6–8, 1088, Hungary
Email: szucsandras@eudens.elte.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04083-0
PII: S 0002-9939(98)04083-0
Keywords: Immersion, multiple points
Received by editor(s): July 4, 1995
Received by editor(s) in revised form: September 2, 1996
Additional Notes: The first author was supported in part by the Russian Foundation for Fundamental Research grant N 96-01-01166a. The second and the third authors were supported by the Hungarian National Science Foundation, Grant No. F-014906 and 4232, respectively
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1998 American Mathematical Society