We define a higher homotopy commutativity of -spaces using the cyclohedra constructed by Bott and Taubes. An -space whose multiplication is homotopy commutative of the -th order is called a -space. We also give combinatorial decompositions of the permuto-associahedra introduced by Kapranov into union of product spaces of the cyclohedra. From the decomposition, we have a relation between the -structures and another higher homotopy commutativity represented by the permuto-associahedra.
Cite this article
Yusuke Kawamoto, Higher Homotopy Commutativity of -spaces and the Cyclohedra. Publ. Res. Inst. Math. Sci. 49 (2013), no. 4, pp. 737–760