• Corpus ID: 16782971

Examples of centralizers in the Artin braid groups

@article{Ivanov2003ExamplesOC,
  title={Examples of centralizers in the Artin braid groups},
  author={Nikolai V. Ivanov},
  journal={arXiv: Geometric Topology},
  year={2003}
}
  • N. V. Ivanov
  • Published 29 June 2003
  • Mathematics
  • arXiv: Geometric Topology
The goal of this paper is to construct examples of centralizers in the Artin braid groups requiring the number of generators quadratic in the number of strings. These examples disprove a recent conjecture of N. Franco and J. Gonzalez-Meneses. 

References

SHOWING 1-10 OF 20 REFERENCES
Automorphisms of surface braid groups
In this paper, we prove that each automorphism of a surface braid group is induced by a homeomorphism of the underlying surface, provided that this surface is a closed, connected, orientable surface
SYSTEMS OF GENERATORS FOR CENTRALIZERS OF RIGID ELEMENTS OF THE BRAID GROUP
The problem of describing centralizers of elements of the braid group was posed by Artin in 1947. An element of the braid group is said to be rigid if it can be represented as a positive word that is
The theory of braids.
  • E. Artin
  • Mathematics
    American scientist
  • 1950
A theory of braids leading to a classification was given in my paper "Theorie der Zopfe" in vol. 4 of the Hamburger Abhandlungen (quoted as Z). Most of the proofs are entirely intuitive. That of the
Über Normalisatoren der Zopfgruppe
Computation of Centralizers in Braid groups and Garside groups
We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. This method, together with the solution of the conjugacy problem given by
Systems of generators for normalizers of certain elements of the braid group, Izvestia AN SSSR, v
  • English translation: Mathematics of the USSR-Izvestia
  • 1984
E-mail: ivanov@math.msu
  • E-mail: ivanov@math.msu
The cohomology ring of the group of dyed braids
  • Mat. Zametki, V
  • 1969
...
...