We construct new knot polynomials. Let V be the standard solid torus in 3-space and let pr be its standard projection onto an annulus. LetM be the space of all smooth oriented knots in V such that the restriction of pr is an immersion (e.g. regular diagrams of a classical knot in the complement of its meridian). There is a canonical one dimensional homology class for each connected component of...

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.

We introduce a new algorithm for computing zigzag persistence, designed in the same spirit as the standard persistence algorithm. Our algorithm reduces a single matrix, maintains an explicit set of chains encoding the persistent homology of the current zigzag, and updates it under simplex insertions and removals. The total worst-case running time matches the usual cubic bound. A noticeable diff...

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...

On the cohomology of BS• the second product · is cup product, which is zero for classes supported on disjoint components. The first product ⊙ is the relatively new transfer product first studied by Strickland and Turner [21], (see Definition 3.1). It is akin to the “induction product” in the representation theory of symmetric groups, which dates back to Young and has been in standard use [9, 22...

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...