On some rational fibrations with nonvanishing Massey products over homogeneous spaces

Tralle, Alexei. "On some rational fibrations with nonvanishing Massey products over homogeneous spaces." Proceedings of the Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1994. [243]-250. <http://eudml.org/doc/220112>.

@inProceedings{Tralle1994,
abstract = {The main result of this brief note asserts, incorrectly, that there exists a rational fibration $S^2 \rightarrow E \rightarrow \mathbb \{C\}P^3$ 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: $ab \ne D(x^2y))$. In fact, for any rational fibration $S^2 \rightarrow E\rightarrow \mathbb \{C\}P^3$ the total space is formal and therefore, in particular, all Massey products in $H^* (E;\mathbb \{Q\})$ 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.},
author = {Tralle, Alexei},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter School; Zdíkov (Czech Republic); Geometry; Physics},
location = {Palermo},
pages = {[243]-250},
publisher = {Circolo Matematico di Palermo},
title = {On some rational fibrations with nonvanishing Massey products over homogeneous spaces},
url = {http://eudml.org/doc/220112},
year = {1994},
}

TY - CLSWK
AU - Tralle, Alexei
TI - On some rational fibrations with nonvanishing Massey products over homogeneous spaces
T2 - Proceedings of the Winter School "Geometry and Physics"
PY - 1994
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [243]
EP - 250
AB - The main result of this brief note asserts, incorrectly, that there exists a rational fibration $S^2 \rightarrow E \rightarrow \mathbb {C}P^3$ 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: $ab \ne D(x^2y))$. In fact, for any rational fibration $S^2 \rightarrow E\rightarrow \mathbb {C}P^3$ the total space is formal and therefore, in particular, all Massey products in $H^* (E;\mathbb {Q})$ 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.
KW - Proceedings; Winter School; Zdíkov (Czech Republic); Geometry; Physics
UR - http://eudml.org/doc/220112
ER -