Symmetric homology of a unital algebra A over a commutative ground ring k has been defined using derived functors and the symmetric bar construction of Fiedorowicz, in an analogous way as cyclic, dihedral or quaternionic homology has been defined. In this paper, it is found that the HS∗(A) admits Dyer-Lashoff homology operations, and indeed, there is a Pontryagin product structure making HS∗(A)...

This text is a preliminary version of material used for a course at the University of Copenhagen, part of ”Workshop and Masterclass on Homological stability” August 26-30, 2013. This lecture concerns the method developped, in collaboration with Aurélien Djament, in [DV10] and used in [Dja12] and [DVa] to compute the stable homology of a family of groups with coefficients given by a polynomial f...

This text is a preliminary version of material used for a course at the University of Copenhagen, part of ”Workshop and Masterclass on Homological stability” August 26-30, 2013. This lecture concerns the method developped, in collaboration with Aurélien Djament, in [DV10] and used in [Dja12] and [DVa] to compute the stable homology of a family of groups with coefficients given by a polynomial f...

A homology stratification is a filtered space with local homology groups constant on strata. Despite being used by Goresky and MacPherson [3] in their proof of topological invariance of intersection homology, homology stratifications do not appear to have been studied in any detail and their properties remain obscure. Here we use them to present a simplified version of the Goresky–MacPherson pr...

We compute the equivariant $KO$-homology of classifying space for proper actions $\textrm{SL}_3(\mathbb{Z})$ and $\textrm{GL}_3(\mathbb{Z})$. also Bredon homology $K$-homology spaces $\textrm{PSL}_2(\mathbb{Z}[\frac{1}{p}])$ $\textrm{SL}_2(\mathbb{Z}[\frac{1}{p}])$ each prime $p$. Finally, we prove Unstable Gromov-Lawson-Rosenberg Conjecture a large class groups whose maximal finite subgroups a...

Idiograms are graphical representations in which chromosomes appear ordered by their relative size, homology groups, and the presence of cytogenetic landmarks such as centromeres, secondary constrictions, banding patterns. They have become crucial elements research. Here, we describe a simple protocol for spreadsheet software to draw idiograms map any type sequence onto them. These graphs can b...

We extend Lawrence's representations of the braid groups to relative homology modules, and we show that they are free modules over a Laurent polynomials ring. define homological operators actually provide representation for an integral version $U_q \mathfrak{sl}(2)$. suggest isomorphism between given basis standard tensor products Verma it preserve ring coefficients, action \mathfrak{sl}(2)$, g...

We study Kuperberg invariants for sutured manifolds in the case of a semidirect product an involutory Hopf superalgebra $H$ with its automorphism group $\text{Aut}(H)$. These are topological balanced 3-manifolds endowed homomorphism fundamental into $\text{Aut}(H)$ and possibly $\text{Spin}^c$ structure homology orientation. show that these computed via form Fox calculus that, if is $\mathbb{N}...

A-484954 is a known eEF2K inhibitor with submicromolar IC50 potency. However, the binding mechanism and the crystal structure of the kinase remains unknown. Here, we employ a homology eEF2K model, docking and alchemical free energy simulations to probe the binding mechanism of eEF2K, and in turn, guide the optimization of potential lead compounds. The inhibitor was docked into the ATP-binding s...