2 9 Ja n 20 02 ON RACK COHOMOLOGY

2 5 Ja n 20 02 Degeneration of the Leray spectral sequence for certain geometric quotients

We prove that the Leray spectral sequence in rational cohomology for the quotient map U n,d → U n,d /G where U n,d is the affine variety of equations for smooth hypersurfaces of degree d in P n (C) and G is the general linear group, degenerates at E 2 .

12 11 9 v 2 2 8 Ja n 20 05 Some remarks on Gopakumar - Vafa invariants

We show that Gopakumar-Vafa (GV) invariants can be expressed in terms of the cohomology ring of moduli space of D-branes without reference to the (sl2)L ⊕ (sl2)R action. We also give a simple construction of this action.

/ 02 01 28 9 v 1 3 0 Ja n 20 02 The η ′ → ηππ decay in U ( 3 ) chiral perturbation theory 1

ar X iv : h ep - p h / 02 11 44 9 v 2 1 6 Ja n 20 03 Three - Body Forces in Multiparticle Dynamics : New Sites of Fundamental Dynamics

A manifestation of the three-body forces in multiparticle dynamics is discussed. The minireview of our recent results has been presented.

2 7 Ja n 20 06 HILBERT 90 FOR GALOIS COHOMOLOGY

Assuming the Bloch-Kato Conjecture, we determine precise conditions under which Hilbert 90 is valid for Milnor k-theory and Galois cohomology. In particular, Hilbert 90 holds for degree n when the cohomological dimension of the Galois group of the maximal p-extension of F is at most n.