Whitehead products in moment-angle complexes

• Iriye Kouyemon

  Department of Mathematical Sciences Osaka Prefecture University

• Kishimoto Daisuke

  Department of Mathematics Kyoto University

Abstract

In toric topology, to a simplicial complex 𝐾 with 𝑚 vertices, one associates two spaces, the moment-angle complex 𝒵_𝐾 and the Davis–Januszkiewicz space 𝐷𝐽_𝐾. These spaces are connected by a homotopy fibration 𝒵_𝐾 → 𝐷𝐽_𝐾 → (ℂ𝑃^∞)^𝑚. In this paper, we show that the map 𝒵_𝐾 → 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.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 72 (4), 1239-1257, 2020

  The Mathematical Society of Japan

Keywords

• moment-angle complex
• Davis–Januszkiewicz space
• polyhedral product
• Whitehead product
• fillable complex
• shellable complex

Details

• CRID: 1390004951539550848
• NII Article ID: 130007928963
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/82708270
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL BIB ID: 030704639
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I030704639
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed