Higher Homotopy Commutativity of $H$-spaces and the Cyclohedra | Zendy

Yusuke Kawamoto | Zendy

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

Author(s) -

Yusuke Kawamoto

Publication year - 2013

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.4171/prims/118

Subject(s) - mathematics , commutative property , homotopy , pure mathematics , algebra over a field

We define higher homotopy commutativity of H-spaces using the cyclohedra {Wn}n≥1 constructed by Bott and Taubes. An H-space whose multiplication is homotopy commutative of the n-th order is called a Bn-space. We also give combinatorial decompositions of the permuto-associahedra {KPn}n≥1 introduced by Kapranov into unions of product spaces of cyclohedra. From the decomposition, we have a relation between the Bn-structures and another notion of higher homotopy commutativity represented by the permuto-associahedra. 2010 Mathematics Subject Classification: Primary 55P48, 55P45; Secondary 52B11, 18D10

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