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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On generalizing Boy's surface: constructing a generator of the third stable stem


Author: J. Scott Carter
Journal: Trans. Amer. Math. Soc. 298 (1986), 103-122
MSC: Primary 57R42; Secondary 55Q45, 57N35, 57R65
MathSciNet review: 857435
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Abstract: An analysis of Boy's immersion of the projective plane in $ 3$-space is given via a collection of planar figures. An analogous construction yields an immersion of the $ 3$-sphere in $ 4$-space which represents a generator of the third stable stem. This immersion has one quadruple point and a closed curve of triple points whose normal matrix is a $ 3$-cycle. Thus the corresponding multiple point invariants do not vanish. The construction is given by way of a family of three dimensional cross sections.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0857435-X
PII: S 0002-9947(1986)0857435-X
Article copyright: © Copyright 1986 American Mathematical Society