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Sur une opérade ternaire liée aux treillis de Tamari

Frédéric Chapoton (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

On introduit une opérade anticyclique V définie par une présentation ternaire quadratique. On montre qu’elle admet une base indexée par les arbres binaires planaires. On relie cette construction à la famille des treillis de Tamari ( Y n ) n 0 en construisant un isomorphisme entre V ( 2 n + 1 ) et le groupe de Grothendieck de la catégorie mod Y n qui envoie la base de V ( 2 n + 1 ) sur les classes des modules projectifs et qui transforme la structure anticyclique de V en la transformation de Coxeter de la catégorie dérivée de mod Y n . La dualité...

Surgery on pairs of closed manifolds

Alberto Cavicchioli, Yuri V. Muranov, Fulvia Spaggiari (2009)

Czechoslovak Mathematical Journal

To apply surgery theory to the problem of classifying pairs of closed manifolds, it is necessary to know the subgroup of the group L P * generated by those elements which are realized by normal maps to a pair of closed manifolds. This closely relates to the surgery problem for a closed manifold and to the computation of the assembly map. In this paper we completely determine such subgroups for many cases of Browder-Livesay pairs of closed manifolds. Moreover, very explicit results are obtained in the...

Survey of Oka theory.

Forstnerič, Franc, Lárusson, Finnur (2011)

The New York Journal of Mathematics [electronic only]

Symmetric Hochschild extension algebras

Yosuke Ohnuki, Kaoru Takeda, Kunio Yamagata (1999)

Colloquium Mathematicae

By an extension algebra of a finite-dimensional K-algebra A we mean a Hochschild extension algebra of A by the dual A-bimodule H o m K ( A , K ) . We study the problem of when extension algebras of a K-algebra A are symmetric. (1) For an algebra A= KQ/I with an arbitrary finite quiver Q, we show a sufficient condition in terms of a 2-cocycle for an extension algebra to be symmetric. (2) Let L be a finite extension field of K. By using a given 2-cocycle of the K-algebra L, we construct a 2-cocycle of the K-algebra...

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