Higher homotopy commutativity of H-spaces and homotopy localizations

Kawamoto, Yusuke

doi:10.2140/pjm.2007.231.103

Cited by 3 publications

(2 citation statements)

References 35 publications

(31 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They give the first detailed definition of the sequence of complexes J (n) now known as the multiplihedra, and describe their combinatorial properties. A good review of the combinatorics of their definition is in [18]. This latter reference also shows how the permuto-associahedra can be decomposed by a combinatorial use of the multiplihedra.…”

Section: D D D D D Z Z Z Z Z Z Z Z Z H H H H H H H H Hmentioning

confidence: 99%

Convex hull realizations of the multiplihedra

Forcey

2008

Topology and its Applications

View full text Add to dashboard Cite

We present a simple algorithm for determining the extremal points in Euclidean space whose convex hull is the nth polytope in the sequence known as the multiplihedra. This answers the open question of whether the multiplihedra could be realized as convex polytopes. We use this realization to unite the approach to A n -maps of Iwase and Mimura to that of Boardman and Vogt. We include a review of the appearance of the nth multiplihedron for various n in the studies of higher homotopy commutativity, (weak) n-categories, A ∞ -categories, deformation theory, and moduli spaces. We also include suggestions for the use of our realizations in some of these areas as well as in related studies, including enriched category theory and the graph-associahedra.

show abstract

Section: D D D D D Z Z Z Z Z Z Z Z Z H H H H H H H H Hmentioning

confidence: 99%

Convex hull realizations of the multiplihedra

Forcey

2008

Topology and its Applications

View full text Add to dashboard Cite

show abstract

“…Using the same way as the proof of [15,Proposition 4.1], we have the following proposition: Proposition 6.3. Let n ≥ 1 and 1 ≤ k ≤ n. Assume that X and Y are Castellana-Crespo-Scherer [4, Theorem 7.3] proved that if X is a connected H-space whose cohomology H * (X; F p ) is finitely generated as an algebra over the Steenrod algebra A * p , then the BZ/p-localization L BZ/p (X) is F p -finite and the homotopy fiber F (φ X ) of the universal map φ X : X → L BZ/p (X) is Postnikov.…”

Section: Homotopy Localizationsmentioning

confidence: 97%

Higher homotopy commutativity and the resultohedra

Hemmi¹,

Kawamoto²

2011

J. Math. Soc. Japan

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Quotients of the multiplihedron as categorified associahedra

Forcey

2008

Homology, Homotopy and Applications

View full text Add to dashboard Cite

We describe a new sequence of polytopes which characterize A ∞ -maps from a topological monoid to an A ∞ -space. Therefore each of these polytopes is a quotient of the corresponding multiplihedron. Our sequence of polytopes is demonstrated not to be combinatorially equivalent to the associahedra, as was previously assumed in both topological and categorical literature. They are given the new collective name composihedra. We point out how these polytopes are used to parametrize compositions in the formulation of the theories of enriched bicategories and pseudomonoids in a monoidal bicategory. We also present a simple algorithm for determining the extremal points in Euclidean space whose convex hull is the n th polytope in the sequence of composihedra, that is, the n th composihedron CK(n).

show abstract

Higher homotopy commutativity of H-spaces and homotopy localizations

Cited by 3 publications

References 35 publications

Convex hull realizations of the multiplihedra

Convex hull realizations of the multiplihedra

Higher homotopy commutativity and the resultohedra

Quotients of the multiplihedron as categorified associahedra

Contact Info

Product

Resources

About