We consider a homological expansion of the mapping class group, defined by homology cylinders over a closed oriented surface (up to homology cobordism). These are important model objects in the recent Goussarov-Habiro theory of finite-type invariants of 3-manifolds. We study the structure of this group from several directions: the relative weight filtration of Dennis Johnson, the finite-type fi...

AbstractAbstractWe furnish any category of a universal (co)homology theory. Universal (co)homologies and relative are obtained by showing representability certain functors take values in R-linear abelian categories motivic nature, where R is commutative unitary ring. homology theory on the one point yields “hieratic” R-modules, i.e. indization Freyd’s free R. Grothendieck ∂-functors satellite r...

We use instanton numbers to: (i) stratify moduli of vector bundles, (ii) calculate relative homology of moduli spaces and (iii) distinguish curve singularities.

In their 2012 paper, Bobadilla and Koll\'ar studied topological conditions which guarantee that a proper map of complex algebraic varieties is or differentiable fibration. They also asked whether certain finiteness property on the relative covering space can imply this we answer positively integral homology version question in case abelian varieties, rational compact ball quotients. We propose ...

conclusions based on the location of detected rccs in the structure of hbv proteins, it was found that these rccs may have a critical role in correct folding of hbv proteins and can be considered as drug targets. the results of this study provide new and deep perspectives about structure of hbv proteins for further researches and designing new drugs for treatment of hbv. results the pfam search...

Shake slice generalizes the notion of a link, naturally extending shake knots to links. There is also relative version, concordance, that link concordance. We show if two links are concordant, then their zero surgery manifolds homology cobordant. Then we give several obstructions being slice; for instance, Arf invariants vanish both and each component. Finally bounds disjoint disks in 4-ball he...

Homology can have different meanings for different kinds of biologists. A phylogenetic view holds that homology, defined by common ancestry, is rigorously identified through phylogenetic analysis. Such homologies are taxic homologies (=synapomorphies). A second interpretation, "biological homology" emphasizes common ancestry through the continuity of genetic information underlying phenotypic tr...

The Peiffer product of groups first arose in work of J.H.C. Whitehead on the structure of relative homotopy groups, and is closely related to problems of asphericity for two-complexes. We develop algebraic methods for computing the second integral homology of a Peiffer product. We show that a Peiffer product of superperfect groups is superperfect, and determine when a Peiffer product of cyclic ...

We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence modules, and show that they contain equivalent information. We explain how one can use the existing algorithm for persistent homology to process any of the four modules, and relate it to a recently introduc...