Hess and Shipley defined an invariant of coalgebra spectra called topological coHochschild homology, Bohmann–Gerhardt–Høgenhaven–Shipley–Ziegenhagen developed a coBökstedt spectral sequence to compute the homology $$\mathrm {coTHH}$$ for coalgebras over sphere spectrum. We construct relative study any commutative ring spectrum R. Further, we use algebraic structures in this complete some calcul...

We prove that Khovanov homology detects the trefoils. Our proof incorporates an array of ideas in Floer and contact geometry. It uses open books; invariants we defined instanton setting; a bypass exact triangle sutured homology, proven here; Kronheimer Mrowka's spectral sequence relating with singular knot homology. As byproduct, also strengthen result Mrowka on $SU(2)$ representations group.

objective: crispr/cas9 technology provides a powerful tool for targeted modification of genomes. in this system, a donor dna harboring two flanking homology arms is mostly used for targeted insertion of long exogenous dna. here, we introduced an alternative design for the donor dna by incorporation of a single short homology arm into a circular plasmid. materials and methods: in this experiment...

modeling and simulation techniques are now widely used alongside with their experimental counterparts in order to complement them, or sometimes to bring first insights into the possible outcome of experiments. “modeling” is a general word that could encompass a wide range of methods that could be applied to a variety of subjects and problems. here, the use of selected molecular modeling methods...

The purpose of this paper is to explore the relationship between the cyclic homology and cohomology theories of Connes [9-11], see also Loday and Quillen [20], and "IF equivariant homology and cohomology theories. Here II" is the circle group. The most general results involve the definitions of the cyclic homology of cyclic chain complexes and the notions of cyclic and cocyclic spaces so precis...

The purpose of these notes is to define an equivalence between the natural homology theories associated to operads and the homology of functors over certain categories of operators (PROPs) related to operads.