INTRODUCTION ix

They show that, similarly to the Connes-Moscovici Hopf algebra, this super

Hopf algebra can be realized as a bicrossed product.

9. V. Mathai and S. Wu “Analytic torsion of Z2-graded elliptic complexes.”

This paper provides a construction of the analytic torsion for arbitrary Z2-

graded elliptic complexes. It extends the construction of the analytic torsion for

twisted de Rham complex described in the previous work of the authors. As an

illustration an analytic torsion of twisted Dolbeault complexes is deﬁned. The

authors also discuss applications of their results to topological ﬁeld theories.

10. B. Monthubert and V. Nistor “The K-groups and the index theory of

certain comparison

C∗-algebras.”

In this paper the authors consider a comparison algebra for a complete

Riemannian manifold which is the interior of a manifold with corners. This

is an algebra generated by the 0-order operators which are compositions of

diﬀerential operators with the inverse powers of the Laplacian. Relating this

algebra to the algebra of pseudodiﬀerential operators on a suitable groupoid,

they perform calculations of the K-theory of this algebra and apply it to the

index problems.

11. H. Moriyoshi and P. Piazza “Relative pairings and the Atiyah-Patodi-

Singer index formula for the Godbillon-Vey cocycle.”

This paper outlines the authors’ approach to the extension of the Moriyoshi-

Natsume explicit formula for the pairing between the Godbillon-Vey cyclic co-

homology class and the K-theory index class of the longitudinal Dirac operator

to foliated bundles on the manifolds with boundary.

12. A. N´ emethi “Two exact sequences for lattice cohomology.”

In the earlier work the author introduced lattice cohomology with the goal

of providing a combinatorial description of the Heegaard–Floer homology of

Ozsv´ ath and Szab´ o for the links of normal surface singularities. This has been

accomplished for several classes of examples but remains a conjecture in gen-

eral. In the meantime, the lattice cohomology has become an important tool

in studying links of singularities in its own right. This paper develops further

properties of the lattice cohomology.

13. B. Rangipour “Cup products in Hopf cyclic cohomology with coeﬃ-

cients in contramodules.”

This paper gives a reﬁnement of the cup product construction in Hopf

cyclic cohomology, deﬁned in the previous work of M. Khalkhali and the author.

This construction is particularly useful for study of the dependance of the cup

product on the coeﬃcients.

14. M. Wodzicki “Algebras of p-symbols, noncommutative p-residue, and

the Brauer group”

This paper introduces the algebra of p-symbols, a characteristic p ana-

logue of the algebra of pseudodiﬀerential symbols. The author shows that these

algebras have some remarkable properties and gives a construction of the non-

commutative residue for these algebras. Using elementary but subtle means the

author obtains deep and interesting results.