We define the slope of a colored link in an integral homology sphere, associated to admissible characters on group. Away from certain singular locus, slope is rational function which can be regarded as multivariate gen

In view of the problem portal support a slope, this paper summarizes four arch barrings, their main structure characteristics and disadvantages are analyzed, then new design in-situ reinforced concrete barring is developed for slope mouths, cost materials wage pitmen determined by comparing several structures used to mouths inclined shafts.

We show that there exists an infinite family of pairwise non-isotopic Legendrian knots in the standard contact 3-sphere whose Stein traces are equivalent. This is first example such phenomenon. Different constructions developed article, including a annulus twist, explicit Weinstein handlebody equivalences, and discussion on dualizable patterns setting. These can be used to systematically constr...