Ricerc@Sapienza

A reformulation of the Hodge index theorem within the framework of Atiyah’s L2-index theory is provided. More precisely, given a compact Kähler manifold (M, h) of even complex dimension 2m, we prove that σ(M)=∑p,q=02m(-1)ph(2),Γp,q(M)where σ(M) is the signature of M and h(2),Γp,q(M) are the L2-Hodge numbers of M with respect to a Galois covering having Γ as group of deck transformations. Likewise we also prove an L2-version of the Frölicher index theorem, see (3).

Let (M,ω,J,g) be a non-compact almost Kähler manifold. In this paper we provide various criteria that assure that ω k induces a non trivial class in the reduced L p maximal/minimal cohomology of (M,g). Furthermore in the last part we explore some topological applications of our results.

Peptides are versatile building blocks that have been extensively used as peptide-based organizers to generate bioinspired hybrid materials. Among them, those peptides characterized by regularly alternating enantiomeric sequences (L,D-peptides) have attracted much interest. Their structures, which are not accessible to the corresponding homochiral peptides, have been exploited to achieve hybrid conjugates, the chemical and structural properties of which can be predetermined by correct design.