@article {Hưng2014251, title = {On the vanishing of the Lannes{\textendash}Zarati homomorphism}, journal = {Comptes Rendus Mathematique}, volume = {352}, number = {3}, year = {2014}, pages = {251 - 254}, abstract = {Abstract The conjecture on spherical classes states that the Hopf invariant one and the Kervaire invariant one classes are the only elements in H ⁎ ( Q 0 S 0 ) belonging to the image of the Hurewicz homomorphism. The Lannes{\textendash}Zarati homomorphism is a map that corresponds to an associated graded (with a certain filtration) of the Hurewicz map. The algebraic version of the conjecture predicts that the s-th Lannes{\textendash}Zarati homomorphism vanishes in any positive stems for s \> 2 . In the article, we prove the conjecture for the fifth Lannes{\textendash}Zarati homomorphism.}, issn = {1631-073X}, doi = {http://dx.doi.org/10.1016/j.crma.2014.01.013}, url = {http://www.sciencedirect.com/science/article/pii/S1631073X14000351} }