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

 

Immersed codimension one projective spaces in spherical space forms


Author: J. Scott Carter
Journal: Proc. Amer. Math. Soc. 105 (1989), 254-257
MSC: Primary 57S25; Secondary 57R42, 57R95, 57S17
MathSciNet review: 946623
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Abstract: Let a finite group of order $ 2k$ act freely on an $ n$-sphere. Then there is a generic immersion of an $ (n - 1)$-dimensional projective space in the quotient space; the induced homomorphism on the fundamental group is injective. Any such immersion has at least $ \left( {\begin{array}{*{20}{c}} k \\ n \\ \end{array} } \right)\frac{1}{k}$ $ n$-tuple points. A better lower bound is also given.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0946623-8
PII: S 0002-9939(1989)0946623-8
Article copyright: © Copyright 1989 American Mathematical Society