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October, 2020 Whitehead products in moment-angle complexes
Kouyemon IRIYE, Daisuke KISHIMOTO
J. Math. Soc. Japan 72(4): 1239-1257 (October, 2020). DOI: 10.2969/jmsj/82708270

Abstract

In toric topology, to a simplicial complex $K$ with $m$ vertices, one associates two spaces, the moment-angle complex $\mathcal{Z}_K$ and the Davis–Januszkiewicz space $DJ_K$. These spaces are connected by a homotopy fibration $\mathcal{Z}_K \to DJ_K \to (\mathbb{C} P^{\infty})^m$. In this paper, we show that the map $\mathcal{Z}_K \to DJ_K$ is identified with a wedge of iterated (higher) Whitehead products for a certain class of simplicial complexes $K$ including dual shellable complexes. We will prove the result in a more general setting of polyhedral products.

Funding Statement

The authors were partly supported by JSPS KAKENHI (No. 26400094 and No. 17K05248).

Citation

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Kouyemon IRIYE. Daisuke KISHIMOTO. "Whitehead products in moment-angle complexes." J. Math. Soc. Japan 72 (4) 1239 - 1257, October, 2020. https://doi.org/10.2969/jmsj/82708270

Information

Received: 20 May 2019; Published: October, 2020
First available in Project Euclid: 25 March 2020

MathSciNet: MR4165931
Digital Object Identifier: 10.2969/jmsj/82708270

Subjects:
Primary: 55Q15
Secondary: 55P15

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 4 • October, 2020
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