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Barbu Berceanu

  1. Fundamental Group of Desargues Configuration Spaces.

    Чт, 02/10/2011 - 16:01 — SomNambul
    Authors: Saima Parveen, Barbu Berceanu
    Subjects: Geometric Topology
    Abstract

    We compute the fundamental group of various spaces of Desargues
    configurations in complex projective spaces: planar and non-planar
    configurations, with a fixed center and also with an arbitrary center.

  2. Fibonacci numbers and positive braids.

    Пнд, 05/10/2010 - 15:01 — SomNambul
    Authors: Barbu Berceanu, Rehana Ashraf, Ayesha Riasat
    Subjects: Combinatorics
    Abstract

    The paper contains enumerative combinatorics for positive braids, square free
    braids, and simple braids, emphasizing connections with classical Fibonacci
    sequence. The simple subgraph of the Cayley graph of the braid group is
    analyzed in the final part.

  3. Recurrence relation for HOMFLY polynomial and rational specializations.

    Пт, 03/05/2010 - 16:01 — SomNambul
    Authors: Barbu Berceanu, Rehana Ashraf
    Subjects: Geometric Topology
    Abstract

    Turning the skein relation for HOMFLY into a Fibonacci recurrence, we prove
    that there are only three rational specializations of HOMFLY polynomial:
    Alexander-Conway, Jones, and a new one. Using the recurrence relation, we find
    general and relative expansion formulae and rational generating functions for
    Alexander-Conway polynomial and the new polynomial, which reduce the
    computations to closure of simple braids, a subset of square free braids;
    HOMFLY polynomials of these simple braids are also computed. Algebraic
    independence of these three polynomials is proved.

  4. Braid groups in complex projective spaces.

    Пт, 02/12/2010 - 16:01 — SomNambul
    Authors: Saima Parveen, Barbu Berceanu
    Subjects: Geometric Topology
    Abstract

    We describe the fundamental groups of ordered and unordered k point sets in
    complex projective space of dimension n generating a projective subspace of
    dimension i. We apply these to study connectivity of more complicated
    configurations of points.

Math-arch

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