We develop the notion of the good pants homology and show that it agrees with the standard homology on closed surfaces (good pants are pairs of pants whose cuffs have the length nearly equal to some large number R > 0). Combined with our previous work on the Surface Subgroup Theorem [5], this yields a proof of the Ehrenpreis conjecture.

We develop the notion of the good pants homology and show that it agrees with the standard homology on closed surfaces (good pants are pairs of pants whose cuffs have the length nearly equal to some large number R > 0). Combined with our previous work on the Surface Subgroup Theorem [6], this yields a proof of the Ehrenpreis conjecture.

Using derived categories of equivariant coherent sheaves, we construct a categorification of the tangle calculus associated to sl(2) and its standard representation. Our construction is related to that of Seidel-Smith by homological mirror symmetry. We show that the resulting doubly graded knot homology agrees with Khovanov homology.

The contact homology, rigorously defined in [7], is computed for a number of Legendrian submanifolds in standard contact (2n+1)-space. The homology is used to detect infinite families of pairwise non-isotopic Legendrian n-spheres, n-tori, and surfaces which are indistinguishable using previously known invariants.

Background: This study aimed at analyzing microbial contamination in medical equipment, environment, and staff of a gastroenterology unit.    Methods: Samples of gastrointestinal imaging devices, the environment, and staff were collected using standard swab-rinse technique and biochemical or molecular characteristics of the isolates, their susceptibility to antibiotics, and similarit...

Abstract We compute a presentation of the fundamental group higher-rank graph using coloured description graphs developed by third author. groups several examples from literature. Our results fit naturally into suite known geometrical about when we show that abelianization is homology group. end with calculation which gives non-standard Klein bottle to one normally found in

In this short note, we discuss certain examples of Legendrian submanifolds, whose linearized contact (co)homology groups over integers have non-vanishing algebraic torsion. More precisely, for a given arbitrary finitely generated abelian group [Formula: see text] and positive integer text], construct submanifolds the standard vector space text]th computed with respect to augmentation is isomorp...

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...