On some rational fibrations with nonvanishing Massey products over homogeneous spaces

Tralle, Alexei

Proceedings of the Winter School "Geometry and Physics", GDML_Books, (1994), p. [243]-250 / Harvested from

Résumé

The main result of this brief note asserts, incorrectly, that there exists a rational fibration $S^{2} \to E \to ℂ P^{3}$ 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: $a b \neq D (x^{2} y))$ . In fact, for any rational fibration $S^{2} \to E \to ℂ P^{3}$ the total space is formal and therefore, in particular, all Massey products in $H^{*} (E; ℚ)$ are zero. This latter assertion can be seen to be true by writing the minimal model of such a fibration and then observing that all candidates for the total space are formal.

MR MR1344015 | Zbl 0859.55012

EUDML-ID : urn:eudml:doc:220112
Mots clés:

@article{701559,
     title = {On some rational fibrations with nonvanishing Massey products over homogeneous spaces},
     booktitle = {Proceedings of the Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1994},
     pages = {[243]-250},
     mrnumber = {MR1344015},
     zbl = {0859.55012},
     url = {http://dml.mathdoc.fr/item/701559}
}

Tralle, Alexei. On some rational fibrations with nonvanishing Massey products over homogeneous spaces, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books,  (1994), pp. [243]-250. http://gdmltest.u-ga.fr/item/701559/