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Higher homotopy commutativity of -spaces and the permuto-associahedra
In this paper, we give a combinatorial definition of a higher homotopy commutativity of the multiplication for an A n A_n -space. To give the definition, we use polyhedra called the permuto-associahedra which are constructed by Kapranov. We also show that if a connected A p A_p -space has the finite...
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| Published in: | Transactions of the American Mathematical Society 2004-10, Vol.356 (10), p.3823-3839 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | In this paper, we give a combinatorial definition of a higher homotopy commutativity of the multiplication for an
A
n
A_n
-space. To give the definition, we use polyhedra called the permuto-associahedra which are constructed by Kapranov. We also show that if a connected
A
p
A_p
-space has the finitely generated mod
p
p
cohomology for a prime
p
p
and the multiplication of it is homotopy commutative of the
p
p
-th order, then it has the mod
p
p
homotopy type of a finite product of Eilenberg-Mac Lane spaces
K
(
Z
,
1
)
K(\mathbb {Z},1)
s,
K
(
Z
,
2
)
K(\mathbb {Z},2)
s and
K
(
Z
/
p
i
,
1
)
K(\mathbb {Z}/p^i,1)
s for
i
≥
1
i\ge 1
. |
|---|---|
| ISSN: | 0002-9947 1088-6850 |
| DOI: | 10.1090/S0002-9947-04-03647-5 |