Related papers: Reflexive homology

Symmetric homology is a natural generalization of cyclic homology, in which symmetric groups play the role of cyclic groups. In the case of associative algebras, the symmetric homology theory was introduced by Z. Fiedorowicz \cite{F} and…

To any Hopf algebra H we associate two commutative Hopf algebras, which we call the first and second lazy homology Hopf algebras of H. These algebras are related to the lazy cohomology groups based on the so-called lazy cocycles of H by…

For a commutative ring $R$ with a unit, an $R$-homology rose is a topological space whose homology groups with $R$-coefficients agree with those of a bouquet of cirlces. In this paper, we study some special properties of covering spaces and…

This article studies the categorical setting of Abramsky, Haghverdi, and Scott's untyped linear combinatory algebras, and relates this to more recent work of Abramsky and Heunen on Frobenius algebras in the infinitary setting. The key to…

In this article we study higher homological properties of $n$-levelled algebras and connect them to properties of the underlying graphs. Notably, to each $2$-representation-finite quadratic monomial algebra $\Lambda$ we associate a…

We characterise reflexive DG-categories, as introduced by Kuznetsov and Shinder, as the reflexive objects in the closed symmetric monoidal category of DG-categories localised at Morita equivalences. As consequences, we show that the…

The homology cobordism group of homology cylinders is a generalization of both the mapping class group of surfaces and the string link concordance group. We consider extensions of Johnson homomorphisms of a mapping class group, Milnor…

We extend Ravenel-Wilson Hopf ring techniques to $C_2$-equivariant homotopy theory. Our main application and motivation is a computation of the $RO(C_2)$-graded homology of $C_2$-equivariant Eilenberg-MacLane spaces. The result we obtain…

In this paper we give an example of a proper standard C*-algebra (a proper C*-subalgebra of B(H) containing C(H)) whose automorphism and isometry groups are topologically reflexive. Furthermore, we prove that in the case of extensions of…

This paper continues the research of the author on the homology of cubical and semi-cubical sets with coefficients in systems of objects. The main result is the theorem that the homology of cubical sets with coefficients in contravariant…

For commutative algebras there are three important homology theories, Harrison homology, Andre-Quillen homology and Gamma-homology. In general these differ, unless one works with respect to a ground field of characteristic zero. We show…

The homology cobordism group of homology cylinders is a generalization of the mapping class group and the string link concordance group. We study this group and its filtrations by subgroups by developing new homomorphisms. First, we define…

We use Heegaard Floer homology to define an invariant of homology cobordism. This invariant is isomorphic to a summand of the reduced Heegaard Floer homology of a rational homology sphere equipped with a spin structure and is analogous to…

A spectral sequence calculating the homology groups of some spaces of maps equivariant under compact group actions is described. For the main example, we calculate the rational homology groups of spaces of even and odd maps $S^m \to S^M$,…

We introduce a commutative product of degree $-n$ on the homology $H_\ast(X)$ of an $n$-dimensional special cubical set $X$ and lift it on the free loop homology $H_\ast(\Lambda M)$ for $M=|X|$ to be the geometric realization. These…

We know that coalgebra measurings behave like generalized maps between algebras. In this note, we show that coalgebra measurings between commutative algebras induce morphisms between higher order Hochschild homology groups of algebras. By…

The codomain category of a generalized homology theory is the category of modules over a ring. For an abelian category A, an A-valued (generalized) homology theory is defined by formally replacing the category of modules with the category…

Let X be a simply connected space and k a commutative ring. Goodwillie, Burghelea and Fiedorowiscz proved that the Hochschild cohomology of the singular chains on the pointed loop space HH^{*}S_*(\Omega X) is isomorphic to the free loop…

In the paper we describe complexes whose homologies are naturally isomorphic to the first term of the Vassiliev spectral sequence computing (co)homology of the spaces of long knots in R^d, d>=3. The first term of the Vassiliev spectral…

We show that for any compact connected group G the second cohomology group defined by unitary invariant 2-cocycles on \hat G is canonically isomorphic to H^2(\hat{Z(G)};T). This implies that the group of autoequivalences of the C*-tensor…