Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Higher homotopy commutativity of $H$-spaces and the permuto-associahedra
HTML articles powered by AMS MathViewer

by Yutaka Hemmi and Yusuke Kawamoto PDF
Trans. Amer. Math. Soc. 356 (2004), 3823-3839 Request permission


In this paper, we give a combinatorial definition of a higher homotopy commutativity of the multiplication for an $A_n$-space. To give the definition, we use polyhedra called the permuto-associahedra which are constructed by Kapranov. We also show that if a connected $A_p$-space has the finitely generated mod $p$ cohomology for a prime $p$ and the multiplication of it is homotopy commutative of the $p$-th order, then it has the mod $p$ homotopy type of a finite product of Eilenberg-Mac Lane spaces $K(\mathbb {Z},1)$s, $K(\mathbb {Z},2)$s and $K(\mathbb {Z}/p^i,1)$s for $i\ge 1$.
Similar Articles
Additional Information
  • Yutaka Hemmi
  • Affiliation: Department of Mathematics, Faculty of Science, Kochi University, Kochi 780-8520, Japan
  • Email:
  • Yusuke Kawamoto
  • Affiliation: Department of Mathematics, National Defense Academy, Yokosuka 239-8686, Japan
  • Email:
  • Received by editor(s): November 27, 2001
  • Published electronically: May 11, 2004

  • Dedicated: Dedicated to the memory of Professor Masahiro Sugawara
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 3823-3839
  • MSC (2000): Primary 55P45, 55P48; Secondary 55P15, 52B11
  • DOI:
  • MathSciNet review: 2058507