Koszulity of cohomology = K ( π ,1)-ness + quasi-formality

Hochschild Cohomology versus De Rham Cohomology without Formality Theorems

We exploit the Fedosov-Weinstein-Xu (FWX) resolution proposed in q-alg/9709043 to establish an isomorphism between the ring of Hochschild cohomology of the quantum algebra of functions on a symplectic manifold M and the ring H(M,C((~))) of De Rham cohomology of M with the coefficient field C((~)) without making use of any version of formality theorem. We also show that the Gerstenhaber bracket ...

Renormalization of K + K − → π 0 π + π −

Measurement of B ( K + → π + νν ) 1

The experimental measurement of K→πνν is reviewed. New results from experiment E787 at BNL are presented: with data from 1995–97 the branching ratio has been measured to be B(K→πνν ) = (1.5 −1.2) × 10 . The future prospects for additional data in this mode are examined.

Formality of Equivariant Intersection Cohomology of Algebraic Varieties

We present a proof that the equivariant intersection cohomology of any complete algebraic variety acted by a connected algebraic group G is a free module over H∗(BG).

Complex Reflection Arrangements Are K ( Π , 1 )

Let V be a finite dimensional complex vector space and W ⊆ GL(V ) be a finite complex reflection group. Let V reg be the complement in V of the reflecting hyperplanes. We prove that V reg is a K(π, 1) space. This was predicted by a classical conjecture, originally stated by Brieskorn for complexified real reflection group. The complexified real case follows from a theorem of Deligne and, after ...