Higher homotopy commutativity and the resultohedra

We define a higher homotopy commutativity for the multiplication of a topological monoid. To give the definition, we use the resultohedra constructed by Gelfand, Kapranov and Zelevinsky. Using the higher homotopy commutativity, we have necessary and sufficient conditions for the classifying space of...

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Bibliographic Details
Published in:Journal of the Mathematical Society of Japan 2011, Vol.63 (2), p.443-471
Main Authors: HEMMI, Yutaka, KAWAMOTO, Yusuke
Format: Article
Language:English
Subjects:
52B11
55P35
55P48
55R35
C_k(n)-spaces
higher homotopy commutativity
resultohedra
topological monoids
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Summary:We define a higher homotopy commutativity for the multiplication of a topological monoid. To give the definition, we use the resultohedra constructed by Gelfand, Kapranov and Zelevinsky. Using the higher homotopy commutativity, we have necessary and sufficient conditions for the classifying space of a topological monoid to have a special structure considered by Félix, Tanré and Aguadé. It is also shown that our higher homotopy commutativity is rationally equivalent to the one of Williams.
ISSN:0025-5645
1881-2333
DOI:10.2969/jmsj/06320443