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Projective product spaces | Donald M. Davis
; | Date: |
4 Aug 2009 | Abstract: | Let nbar=(n_1,...,n_r). The quotient space P_nbar:=(S^{n_1x...xS^{n_r))/(x ~
-x)is what we call a projective product space. We determine the integral
cohomology ring and the action of the Steenrod algebra. We give a splitting of
Sigma P_nbar in terms of stunted real projective spaces, and determine the
ring K^*(P_nbar). We relate the immersion dimension and span of P_nbar to the
much-studied sectioning question for multiples of the Hopf bundle over real
projective spaces. We show that the immersion dimension of P_nbar depends only
on min(n_i), sum n_i, and r. We also determine exactly when P_nbar is
parallelizable. | Source: | arXiv, 0908.0525 | Services: | Forum | Review | PDF | Favorites |
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