On the vanishing of the Lannes–Zarati homomorphism

Tiêu đềOn the vanishing of the Lannes–Zarati homomorphism
Loại công bốJournal Article
Năm xuất bản2014
Tác giảHưng, NHV, Quỳnh, VTN, Tuấn, NA
Tạp chíComptes Rendus Mathematique
Thể tích352
Trang251 - 254
Tóm tắt

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–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–Zarati homomorphism vanishes in any positive stems for s > 2 . In the article, we prove the conjecture for the fifth Lannes–Zarati homomorphism.