arXiv subjects

Dong T. Triet

Publications and source records attributed to Dong T. Triet.

2 recordsLinked to original sources

arXiv2016

On the mod $p$ Lannes-Zarati homomorphism

The mod $2$ Lannes-Zarati homomorphism was constructed in \cite{Lan-Zar87}, which is considered as a graded associated version of the mod $2$ Hurewicz map in the $E_2$-term of Adams spectral sequence. The map is studied by many authors such as Lannes-Zarati \cite{Lan-Zar87}, H\horn{u}ng \cite{Hung97}, \cite{Hung2001}, \cite{Hung2003}, H\horn{u}ng et. al. \cite{Hung.et.al2014}, Ch\horn{o}n-Tri\'êt \cite{Chon.Triet2014}. In this paper, we construct an analogue $φ_s$ for $p$ odd, and we also investigate the behavior of this map for $s\leq 3$.

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arXiv2016

On behavior of the Lannes-Zarati homomorphism

In this paper, we construct the chain level representation in the lambda algebra of the Lannes-Zarati homomorphism for $\mathbb{F}_2$ as well as for $\tilde{H}^*B\mathbb{Z}/2$. Using this construction, we show that the sixth Lannes-Zarati homomorphism for $\mathbb{F}_2$ is trivial at all stems $t$ for $t\leq 114$. Furthermore, using this method, we also investigate the behavior of the Lannes-Zarati homomorphis for $\tilde{H}^*B\mathbb{Z}/2$ at the homological $s\leq 4$.

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