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. 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.
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