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The purpose of this paper is twofold: first, we extend Saito's filtration on Chow groups, which is a candidate for the conjectural Bloch Beilinson filtration on the Chow groups of a smooth projective variety, from Chow groups to the bivariant Chow groups. In order to do this, we construct cycle class maps from the bivariant Chow groups to bivariant cohomology groups. Secondly, we use our methods to define a bivariant version of Bloch's higher Chow groups. [ABSTRACT FROM AUTHOR]

It is well known that the Hochschild cohomology $H^*(A,A)$ of an associative algebra $A$ admits a G-algebra structure. In this paper we show that the dialgebra cohomology $HY^*(D,D)$ of an associative dialgebra $D$ has a similar structure, which is induced from a homotopy G-algebra structure on the dialgebra cochain complex $CY^*(D,D)$. [ABSTRACT FROM AUTHOR]

Let $p$ be an odd prime number and let $G$ be an extraspecial $p$-group. The purpose of the paper is to show that $G$ has no non-zero essential mod-$p$ cohomology (and in fact that $H^{*}(G,\mathbb{F}_{p})$ is Cohen-Macaulay) if and only if $|G|=27$ and $exp(G)=3$. [ABSTRACT FROM AUTHOR]

We prove the uniqueness of twisted K-theory in both the real and complex cases using the computation of the K-theories of Eilenberg-MacLane spaces due to Anderson and Hodgkin. As an application of our method, we give some vanishing results for actions of Eilenberg-MacLane spaces on K-theory spectra. [ABSTRACT FROM AUTHOR]

A chain complex model for the free loop space of a connected, closed and oriented manifold is presented, and on its homology, the Gerstenhaber and Batalin-Vilkovisky algebra structures are defined and identified with the string topology structures. The gravity algebra on the equivariant homology of the free loop space is also modeled. The construction includes the non-simply connected case, and therefore gives an algebraic and chain level model of Chas-Sullivan's String Topology. [ABSTRACT FROM AUTHOR]