Immersed codimension one projective spaces in spherical space forms
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- by J. Scott Carter PDF
- Proc. Amer. Math. Soc. 105 (1989), 254-257 Request permission
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.References
- J. Scott Carter, Immersed projective planes in lens spaces, Proc. Amer. Math. Soc. 106 (1989), no. 1, 251–260. MR 967483, DOI 10.1090/S0002-9939-1989-0967483-5
- John Milnor, Groups which act on $S^n$ without fixed points, Amer. J. Math. 79 (1957), 623–630. MR 90056, DOI 10.2307/2372566
- Gian-Carlo Rota, On the foundations of combinatorial theory. I. Theory of Möbius functions, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2 (1964), 340–368 (1964). MR 174487, DOI 10.1007/BF00531932
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 254-257
- MSC: Primary 57S25; Secondary 57R42, 57R95, 57S17
- DOI: https://doi.org/10.1090/S0002-9939-1989-0946623-8
- MathSciNet review: 946623