Hochschild cohomology

In this article we study several homology theories of the algebra E ∞ (X) of Whitney functions over a subanalytic set X ⊂ Rn with a view towards noncommutative geometry. Using a localization method going back to Teleman we prove a Hochschild-Kostant-Rosenberg type theorem for E ∞ (X), when X is a regular subset of Rn having regularly situated diagonals. This includes the case of subanalytic X. We also compute the Hochschild cohomology of E ∞ (X) for a regular set with regularly situated diagonals and derive the cyclic and periodic cyclic theories. ...

53p dontetvui 17-01-2013 47 7   Download

In a classic paper, Gerstenhaber showed that first order deformations of an associative k-algebra a are controlled by the second Hochschild cohomology group of a. More generally, any n-parameter first order deformation of a gives, due to commutativity of the cup-product on Hochschild cohomology, a graded algebra morphism Sym• (kn ) → Ext2•bimod (a, a). We prove that any extension aof the n-parameter first order deformation of a to an infinite order formal deformation provides a canonical ‘lift’ of the graded algebra morphism above to a dg-algebra morphism Sym• (kn ) → RHom• ...

17p noel_noel 17-01-2013 54 4   Download

Dedicated to the memory of Barry Johnson, 1937–2002 Abstract The main result of this paper is that the k th continuous Hochschild cohomology groups H k (M, M) and H k (M, B(H)) of a von Neumann factor M ⊆ B(H) of type II1 with property Γ are zero for all positive integers k. The method of proof involves the construction of hyperfinite subfactors with special properties and a new inequality of Grothendieck type for multilinear maps. We prove joint continuity in the · 2 -norm of separately ultraweakly continuous multilinear maps, and combine these results to reduce to...

26p tuanloccuoi 04-01-2013 45 6   Download

Topological Hochschild homology and localization 2. The homotopy groups of T (A|K) 3. The de Rham-Witt complex and TR· (A|K; p) ∗ 4. Tate cohomology and the Tate spectrum 5. The Tate spectral sequence for T (A|K) 6. The pro-system TR· (A|K; p, Z/pv ) ∗ Appendix A. Truncated polynomial algebras References Introduction In this paper we establish a connection between the Quillen K-theory of certain local fields and the de Rham-Witt complex of their rings of integers with logarithmic poles at the maximal ideal.

114p tuanloccuoi 04-01-2013 62 6   Download