JournalsprimsVol. 49, No. 4pp. 737–760

Higher Homotopy Commutativity of HH-spaces and the Cyclohedra

  • Yusuke Kawamoto

    National Defense Academy, Yokosuka, Japan
Higher Homotopy Commutativity of $H$-spaces and the Cyclohedra cover

Abstract

We define a higher homotopy commutativity of HH-spaces using the cyclohedra {Wn}n1\{W_n\}_{n\ge 1} constructed by Bott and Taubes. An HH-space whose multiplication is homotopy commutative of the nn-th order is called a BnB_n-space. We also give combinatorial decompositions of the permuto-associahedra {KPn}n1\{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 BnB_n-structures and another higher homotopy commutativity represented by the permuto-associahedra.

Cite this article

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

DOI 10.4171/PRIMS/118