Related papers: Connes-Moscovici characteristic map is a Lie algeb…

We show that the Connes-Moscovici cyclic cohomology of a Hopf algebra equipped with a character has a Lie bracket of degree -2. More generally, we show that a "cyclic operad with multiplication" is a cocyclic module whose cohomology is a…

We discuss a new strategy for the computation of the Hopf-cyclic cohomology of the Connes-Moscovici Hopf algebra $\mathcal{H}_n$. More precisely, we introduce a multiplicative structure on the Hopf-cyclic complex of $\mathcal{H}_n$, and we…

We develop an appropriate dihedral extension of the Connes-Moscovici characteristic map for Hopf *-algebras. We then observe that one can use this extension together with the dihedral Chern character to detect non-trivial $L$-theory classes…

A Frobenius algebra is a finite-dimensional algebra $A$ which comes equipped with a coassociative, counital comultiplication map $\Delta$ that is an $A$-bimodule map. Here, we examine comultiplication maps for generalizations of Frobenius…

A standard combinatorial construction, due to Kontsevich, associates to any A-infinity algebra with an invariant inner product, an inhomogeneous class in the cohomology of the moduli spaces of Riemann surfaces with marked points. We…

We provide examples of non-surjective epimorphisms $H\to K$ in the category of Hopf algebras over a field, even with the additional requirement that $K$ have bijective antipode, by showing that the universal map from a Hopf algebra to its…

Standard combinatorial construction, due to Kontsevich, associates to any $\ai$-algebra with an invariant inner product, an inhomogeneous class in the cohomology of the moduli spaces of Riemann surfaces with marked points. We propose an…

We study the compatibility between the antipode and the preLie product of a Com-PreLie Hopf algebra, that is to say a commutative Hopf algebra with a complementary preLie product, compatible with the product and the coproduct in a certain…

We give explicit formulas for the coproduct and the antipode in the Connes-Moscovici Hopf algebra $\mathcal{H}_{\tmop{CM}}$. To do so, we first restrict ourselves to a sub-Hopf algebra $\mathcal{H}^1_{\tmop{CM}}$ containing the nontrivial…

We study Hopf algebras via tools from geometric invariant theory. We show that all the invariants we get can be constructed using the integrals of the Hopf algebra and its dual together with the multiplication and the comultiplication, and…

We compute the second Hochschild cohomology space $HH^2(\mathcal{H}_1)$ of Connes-Moscovici's Hopf algebra $\mathcal{H}_1$, giving the infinitesimal deformations (up to equivalence) of the associative structure. $HH^2(\mathcal{H}_1)$ is…

We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We…

We define a new cyclic module, dual to the Connes-Moscovici cyclic module, for Hopf algebras, and give a characteristric map for the coaction of Hopf algebras. We also compute the resulting cyclic homology for cocommutative Hopf algebras,…

We obtain two characterizations of the bi-inner Hopf *-automorphisms of a finite-dimensional Hopf C*-algebra, by means of an analysis of the structure of convolution products in this class of Hopf C*-algebra.

We give a construction of cyclic cocycles representing the equivariant characteristic classes of equivariant bundles. Our formulas generalize Connes' Godbillon-Vey cyclic cocycle. An essential tool of our construction is Connes-Moscovici's…

This paper defines a generalization of the Connes-Moscovici Hopf algebra, $\mathcal{H}(1)$ that contains the entire Hopf algebra of rooted trees. A relationship between the former, a much studied object in non-commutative geometry, and the…

REVISED VERSION: We have re-organized the paper, and included some new results. Most important, we prove that the (truncated) Weil complexes compute the cyclic cohomology of the Hopf algebra (see the new Theorem 7.3). We also include a…

Let S be a compact connected oriented surface, whose boundary is connected or empty. A homology cylinder over the surface S is a cobordism between S and itself, homologically equivalent to the cylinder over S. The Y-filtration on the monoid…

Let K be the subgroup of the extended mapping class group, Mod(S), generated by Dehn twists about separating curves. Assuming that S is a closed, orientable surface of genus at least 4, we confirm a conjecture of Farb that Comm(K), Aut(K)…

We show that many noetherian Hopf algebras A have a rigid dualising complex R with R isomorphic to ^{\nu}A^1 [d]. Here, d is the injective dimension of the algebra and \nu is a certain k-algebra automorphism of A, unique up to an inner…