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.

We propose a novel model of street network connectivity which uses method from the field applied topology called “persistent homology”. The output this is pair density functions relative strength and frequency connected components cycles in network. In context, function type, such as motorway or residential, with more significant types providing greater connectivity. are easily interpreted prov...

The Peiier product of groups rst arose in work of J.H.C. White-head 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 Peiier product. We s h o w t h a t a Peiier product of superperfect groups is superperfect, and determine when a Peiier product of cyclic...

Homology-directed repair (HDR) is essential to limit mutagenesis, chromosomal instability (CIN) and tumorigenesis. We have characterized the consequences of HDR deficiency on anaphase, using markers for incomplete chromosome separation: DAPI-bridges and Ultra-fine bridges (UFBs). We show that multiple HDR factors (Rad51, Brca2 and Brca1) are critical for complete chromosome separation during an...

We recently defined an invariant of contact manifolds with convex boundary in Kronheimer and Mrowka's sutured monopole Floer homology theory. Here, we prove that there is isomorphism between Heegaard which identifies our the class by Honda, Kazez Mati\'c latter One consequence Legendrian invariants knot behave functorially respect to Lagrangian concordance. In particular, these provide computab...

1.1. Stable propagation. Let M := UT be the open unit cotangent bundle of the n-dimensional Euclidean torus T = R/Z. We express the elements of M in terms of the canonical coordinates (q1, . . . , qn, p1, . . . , pn), where qi ≡ qi + 1. Thus we identify M with T × D, where D = {|p| < 1} is the open unit ball in R and |v| stands for the Euclidean norm of a vector v ∈ R. Consider the space H of a...

as recent advancements in biology shows, the molecular machines specially proteins, rna and complex molecules play the main role of the so called cell functionality. it means a very big part of the system biology is concerned with the interactions of such molecular components. drug industries and research institutes are trying hard to better understand the concepts underlying these interactions...

Using sutured Floer homology (in short SFH) I will define a polytope inside the second relative cohomology group of a sutured manifold. This is a generalization of the dual Thurston norm polytope of a link-complement studied by Ozsvath and Szabo using link Floer homology. The polytope is maximal dimensional under certain conditions. Moreover, surface decompositions correspond to the faces of th...