Simplicial normalization in the entire cyclic cohomology of Banach algebras

We show that the entire cyclic cohomology of Banach algebras defined by Connes has the simplicial normalization property. A key tool in the proof is the notion and properties of supertraces on the Cuntz algebraQ A. As an example of further applications of this technique, we give a proof of the homotopy invariance of entire cyclic cohomology.Address after 1st October 1995: Department of Mathematics, University of Exeter, North Park Road, Exeter EX4 4QE, U.K.     

Remarks on Two Approaches to the Horizontal Cohomology: Compatibility Complex and the Koszul–Tate Resolution

The Koszul–Tate resolution is described in the context of the geometry of jet spaces and differential equations. The application due to Barnich, Brandt, and Henneaux of this resolution to computing the horizontal cohomology is analyzed. Relations with the Vinogradov spectral sequence are discussed.     

An axiomatic approach to equivariant cohomology theories

This paper presents a translation of a theorem of Cartan into an equivariant setting. This work is largely based on the study of the homotopical algebra in the sense of Quillen of the category of simplicial objects over the category of rationalO _g-vector spaces. The application is a solution to the equivariant commutative cochain problem. This solution is slightly better than the solution obtained earlier by Triantafillou in that the transformation groupG need not be finite.     

A Bivariant Chern character for p-summable quasihomomorphisms

We define a Chern character for p-summable quasihomomorphisms. We study its properties and show that it is compatible with the analytic index. The results are similar to Connes' results on the Chern character on K-homology but the methods are different. This solves most of a problem of Connes.     

A differential geometric setting for BRS transformations and anomalies I

The Becchi-Rouet-Stora relations and the cohomological construction of anomalies of gauge fields are described within the theory of principal connections of smooth vector bundles.     

Duality in algebra and topology

We apply ideas from commutative algebra, and Morita theory to algebraic topology using ring spectra. This allows us to prove new duality results in algebra and topology, and to view (1) Poincaré duality for manifolds, (2) Gorenstein duality for commutative rings, (3) Benson–Carlson duality for cohomology rings of finite groups, (4) Poincaré duality for groups and (5) Gross–Hopkins duality in chromatic stable homotopy theory as examples of a single phenomenon.     

The homotopy limit problem for two-primary algebraic K-theory

We solve the homotopy limit problem for two-primary algebraic K-theory of fields, that is, the Quillen-Lichtenbaum conjecture at the prime 2.     

Generalized local duality,canonical modules,and prescribed bound on projective dimension

We present various approaches to J. Herzog's theory of generalized local cohomology and explore its main aspects, e.g., (non-)vanishing results as well as a general local duality theorem which extends, to a much broader class of rings, previous results by Herzog-Zamani and Suzuki. As an application, we establish a prescribed upper bound for the projective dimension of a module satisfying suitable cohomological conditions, and we derive some freeness criteria and questions of Auslander-Reiten type. Along the way, we prove a new characterization of Cohen-Macaulay modules which truly relies on generalized local cohomology, and in addition we introduce and study a generalization of the notion of canonical module.     

Stereoselective Peterson Olefinations from Bench‐Stable Reagents and N‐Phenyl Imines

The synthesis of bench‐stable α,α‐bis(trimethylsilyl)toluenes and tris(trimethylsilyl)methane is described and their use in stereoselective Peterson olefinations has been achieved with a wide substrate scope. Product stereoselectivity was poor with carbonyl electrophiles (E/Z ～1:1 to 4:1) though this was significantly improved by employing the corresponding substituted N‐benzylideneaniline (up to 99:1) as an alternative electrophile. The olefination byproduct was identified as N,N‐bis(trimethylsilyl)aniline and could be easily separated from product by aqueous acid extraction. Evidence for an autocatalytic cycle has been obtained.     

经典N=2李共形超代数的导子和第二上同调群

研究了经典N=2李共形超代数的导子和第二上同调群的结构,并应用第二上同调群的结果确定了该李共形超代数的泛中心扩张.