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

Carter, J. Scott

doi:10.1090/S0002-9947-1986-0857435-X

On generalizing Boy’s surface: constructing a generator of the third stable stem
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by J. Scott Carter

Trans. Amer. Math. Soc. 298 (1986), 103-122

DOI: https://doi.org/10.1090/S0002-9947-1986-0857435-X

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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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