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$\mathcal{L}$-fillable complexes and Whitehead products in polyhedral products

Hold Date
2021-04-23 17:00〜2021-04-23 18:00
Zoom meeting
Object person
Ryusei Yoshise (Kyushu University)

In toric topology, there are two important spaces associated with a simplicial complex $K$. One is the moment-angle complex denoted by ${¥mathcal Z}_K$, and the other is the Davis-Januszkiewicz space denoted by ${¥mathcal DJ}_K$. They are extended as polyhedral products. Recently, in case when $K$ is totally fillable, Iriye-Kishimoto showed in ¥cite{MR4165931} that the map ${¥mathcal Z_K} (¥ssum ¥underline{X}) ¥rightarrow {¥mathcal DJ_K} (¥ssum ¥underline{X})$ can be divided into a wedge of iterated Whitehead products up to homotopy. In this talk, we extend their result in more general case and construct a simplicial complex which does not satisfies their conditions but ours.