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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Splitting $ S\sp{4}$ on $ {\bf R}P\sp{2}$ via the branched cover of $ {\bf C}P\sp{2}$ over $ S\sp{4}$


Author: Terry Lawson
Journal: Proc. Amer. Math. Soc. 86 (1982), 328-330
MSC: Primary 57M12
MathSciNet review: 667299
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Abstract: The four sphere decomposes as a twisted double $ {N_2}{ \cup _f}{N_2}$, where $ {N_2}$ is the $ 2$-disk bundle over the real projective plane with Euler number 2. In this note the relationship of this splitting to the double branched cover of the complex projective plane over the four sphere as the quotient space under complex conjugation is made explicit.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0667299-7
Keywords: Twisted double, projective plane, involution, branched cover
Article copyright: © Copyright 1982 American Mathematical Society