|
This article is cited in 28 scientific papers (total in 28 papers)
On braid monodromy factorizations
V. M. Kharlamova, Vik. S. Kulikovb a University Louis Pasteur
b Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
We introduce and develop a language of semigroups over the braid groups to study the braid monodromy factorizations (bmf's) of plane algebraic curves and other related objects. As an application, we give a new proof of Orevkov's theorem on the realization of bmf's over a disc by algebraic curves and show that the complexity of such a realization cannot be bounded in terms of the types of factors of the bmf. We also prove that the type of a bmf distinguishes Hurwitz curves with singularities of inseparable type up to $H$-isotopy and $J$-holomorphic
cuspidal curves in $\mathbb{CP}^2$ up to symplectic isotopy.
Received: 23.01.2003
Citation:
V. M. Kharlamov, Vik. S. Kulikov, “On braid monodromy factorizations”, Izv. Math., 67:3 (2003), 499–534
Linking options:
https://www.mathnet.ru/eng/im436https://doi.org/10.1070/IM2003v067n03ABEH000436 https://www.mathnet.ru/eng/im/v67/i3/p79
|
Statistics & downloads: |
Abstract page: | 601 | Russian version PDF: | 216 | English version PDF: | 29 | References: | 82 | First page: | 1 |
|