Small models for chain algebras

Supported by the Deutsche Forschungsgemeinschaft under a Heisenberg grant     

Vertex operators for deformed Virasoro algebra

Vertex operators for the deformed Virasoro algebra are defined, their bosonic representation is constructed, and a difference equation for the simplest vertex operators is described. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 11, 876–881 (10 June 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Iterating the Bar Construction

For a 1-connected space X Adams's bar construction B(C*(X)) describes H*(X) only as a graded module and gives no information about the multiplicative structure. Thus it is not possible to iterate the bar construction in order to determine the cohomology of iterated loop spaces ⁱ X. In this paper for an n-connected pointed space X a sequence of A()-algebra structures , is constructed, such that for each there exists an isomorphism of graded algebras      

Homotopy gerstenhaber algebras: examples and applications

In this paper, we indicate several aspects of the notion of homotopy Gerstenhaber algebras and give some important examples and applications.     

On cochain operations forming hirsch algebras

Cochain operations that determine the structure of Hirsch algebras are characterized.     

Free resolutions for differential modules over differential algebras

A free resolution (R, d + h) → (M, d) for a DG-module (M, d) over a DG-algebra (A, d) is constructed in the sense of a perturbation of the differential in a free bigraded resolution (R, d) → M of the underlying graded module M over an underlying graded algebra A. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 43, Topology and Its Applications, 2006.