1,843 research outputs found
Fundamental groups of some special quadric arrangements
In this work we obtain presentations of fundamental groups of the complements
of three families of quadric arrangements in . The first
arrangement is a union of quadrics, which are tangent to each other at two
common points. The second arrangement is composed of quadrics which are
tangent to each other at one common point. The third arrangement is composed of
quadrics, of them are tangent to the 'th one and each one of the
quadrics is transversal to the other ones.Comment: 21 pages, 12 main figures, appears in Revista Mathematica
Identifying Half-Twists Using Randomized Algorithm Methods
Since the braid group was discovered by E. Artin, the question of its
conjugacy problem has been solved by Garside and Birman, Ko and Lee. However,
the solutions given thus far are difficult to compute with a computer, since
the number of operations needed is extremely large. Meanwhile, random
algorithms used to solve difficult problems such as primality of a number were
developed, and the random practical methods have become an important tool. We
give a random algorithm, along with a conjecture of how to improve its
convergence speed, in order to identify elements in the braid group, which are
conjugated to its generators for a given power. These elements of the braid
group, the half-twists, are important in themselves, as they are the key
players in some geometrical and algebraical methods, the building blocks of
quasipositive braids and they construct endless sets of generators for the
group.Comment: 18 pages, 4 Postscript figures; Last proof read corrections before
printing - Paper accepted for publicatio
Braid Monodromy Factorization and Diffeomorphism Types
In this manuscript we prove that if two cuspidal plane curves have equivalent
braid monodromy factorizations, then they are smoothly isotopic in the plane.
As a consequence of this and the Chisini conjecture, we obtain that if two
discriminant curves (or branch curves in other terminology) of generic
projections (to the plane) of surfaces of general type imbedded in a projective
space by means of a multiple canonical class have equivalent braid monodromy
factorizations, then the surfaces are diffeomorphic (if we consider them as
real 4-folds).Comment: 2 files: TEX file of text and file of figures (gzipped
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