## Higher homotopy commutativity of $H$-spaces and the permuto-associahedra

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

## Abstract:

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 $i\ge 1$.## References

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## Additional Information

**Yutaka Hemmi**- Affiliation: Department of Mathematics, Faculty of Science, Kochi University, Kochi 780-8520, Japan
- Email: hemmi@math.kochi-u.ac.jp
**Yusuke Kawamoto**- Affiliation: Department of Mathematics, National Defense Academy, Yokosuka 239-8686, Japan
- Email: yusuke@nda.ac.jp
- Received by editor(s): November 27, 2001
- Published electronically: May 11, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**356**(2004), 3823-3839 - MSC (2000): Primary 55P45, 55P48; Secondary 55P15, 52B11
- DOI: https://doi.org/10.1090/S0002-9947-04-03647-5
- MathSciNet review: 2058507

Dedicated: Dedicated to the memory of Professor Masahiro Sugawara