The structure of groups with a quasiconvex hierarchy

書誌事項

The structure of groups with a quasiconvex hierarchy

Daniel T. Wise

(Annals of mathematics studies, no. 209)

Princeton University Press, 2021

  • : hardback

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注記

Includes bibliographical references (p. [345]-351) and index

内容説明・目次

内容説明

This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology. Many fundamental new ideas and methodologies are presented here for the first time, including a cubical small-cancellation theory that generalizes ideas from the 1960s, a version of Dehn Filling that functions in the category of special cube complexes, and a variety of results about right-angled Artin groups. The book culminates by establishing a remarkable theorem about the nature of hyperbolic groups that are constructible as amalgams. The applications described here include the virtual fibering of cusped hyperbolic 3-manifolds and the resolution of Baumslag's conjecture on the residual finiteness of one-relator groups with torsion. Most importantly, this work establishes a cubical program for resolving Thurston's conjectures on hyperbolic 3-manifolds, and validates this program in significant cases. Illustrated with more than 150 color figures, this book will interest graduate students and researchers working in geometry, algebra, and topology.

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詳細情報

  • NII書誌ID(NCID)
    BC02563002
  • ISBN
    • 9780691170442
  • LCCN
    2020040293
  • 出版国コード
    us
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Princeton
  • ページ数/冊数
    x, 357 p., [2] p. of plates
  • 大きさ
    25 cm
  • 分類
  • 件名
  • 親書誌ID
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