Displaying similar documents to “Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians”

On some rational fibrations with nonvanishing Massey products over homogeneous spaces

Tralle, Alexei

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The main result of this brief note asserts, incorrectly, that there exists a rational fibration S 2 → E → ℂ P 3 whose total space admits nonzero Massey products. The methods used would be appropriate for showing results of this kind, if the circumstances were to allow for it. Unfortunately the author makes a simple, but nonetheless fatal, computational error in his calculation that ostensibly shows the existence of a nonzero Massey product (p. 249, 1.13: a b ≠ D ( x 2 y ) ) . In fact, for any rational fibration S 2 → E → ℂ P 3 the...

Towards one conjecture on collapsing of the Serre spectral sequence

Markl, Martin

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[For the entire collection see Zbl 0699.00032.] A fibration F → E → B is called totally noncohomologuous to zero (TNCZ) with respect to the coefficient field k, if H * ( E ; k ) → H * ( F ; k ) is surjective. This is equivalent to saying that π 1 ( B ) acts trivially on H * ( F ; k ) and the Serre spectral sequence collapses at E 2 . S. Halperin conjectured that for c h a r ( k ) = 0 and F a 1-connected rationally elliptic space (i.e., both H * ( F ; 𝒬 ) and π * ( F ) ⊗ 𝒬 are finite dimensional) such that H * ( F ; k ) vanishes in odd degrees, every fibration F → E → B is TNCZ. The author proves this...