# Higher Homotopy Commutativity of $H$-spaces and the Cyclohedra

### Yusuke Kawamoto

National Defense Academy, Yokosuka, Japan

## Abstract

We define a higher homotopy commutativity of $H$-spaces using the cyclohedra $\{W_n\}_{n\ge 1}$ constructed by Bott and Taubes. An $H$-space whose multiplication is homotopy commutative of the $n$-th order is called a $B_n$-space. We also give combinatorial decompositions of the permuto-associahedra $\{KP_n\}_{n\ge 1}$ introduced by Kapranov into union of product spaces of the cyclohedra. From the decomposition, we have a relation between the $B_n$-structures and another higher homotopy commutativity represented by the permuto-associahedra.

## Cite this article

Yusuke Kawamoto, Higher Homotopy Commutativity of $H$-spaces and the Cyclohedra. Publ. Res. Inst. Math. Sci. 49 (2013), no. 4, pp. 737–760

DOI 10.4171/PRIMS/118