1,721,017 research outputs found
Criterion of Hurwitz equivalence for quasipositive factorizations of 3-braids
Full text linkWe consider the Hurwitz action on quasipositive factorizations of a 3-braid. In a previous paper, for any given 3-braid we described a certain finite set which contains at least one representative of each orbit. Here we give an algorithm to decide if two elements of this finite set belong to the same orbit.6 page
Algorithmic recognition of quasipositive braids of algebraic length two
Full text linkWe give an algorithm to decide if a given braid is a product of two factors which are conjugates of given powers of standard generators of the braid group. The same problem is solved in a certain class of Garside groups including Artin-Tits groups of spherical type. The solution is based on the Garside theory and, especially, on the theory of cyclic sliding developed by Gebhardt and Gonzalez-Meneses. We show that if a braid is of the required form, then any cycling orbit in its sliding circuit set in the dual Garside structure contains an element for which this fact is immediately seen from the left normal form.25 pages, 1 figur
Markov trace on Funar algebra
Full text linkFunar algebra is the quotient of the group algebra over a ring of the braid group by two cubic relations: and another one which involves and . The universal Markov trace on is the quotient map of to its quotient (as a -module) by trace relations and by Markov relations , for . It is easy to check that the quotient is of the form for some ideal (i. e. that the trace is determined by ). We give an algorithm to compute the ideal and we present the result of computations in some special cases. In the last section we discuss some properties of the resulting link invariant. This invariant for , detects the chirality of the knots and and it distinguish many other pairs of knots with equal HOMFLY polynomials.23 pages, 5 figures, 3 table
On the hyperbolicity locus of a real curve
Full text linkGiven a real algebraic curve in the projective 3-space, its hyperbolicity locus is the set of lines with respect to which the curve is hyperbolic. We give an example of a smooth irreducible curve whose hyperbolicity locus is disconnected but the connected components are not distinguished by the linking numbers with the connected components of the curve.4 pages, 3 figure
The Agnihotri--Woodward--Belkale polytope and Klyachko cones
No full textOriginal Russian Text © S. Yu. Orevkov, Yu. P. Orevkov, 2010, published in Matematicheskie Zametki, 2010, Vol. 87, No. 1, pp. 101-107International audienc
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