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Braid Monodromy of Algebraic Curves

José Ignacio Cogolludo-Agustín (2011)

Annales mathématiques Blaise Pascal

These are the notes from a one-week course on Braid Monodromy of Algebraic Curves given at the Université de Pau et des Pays de l’Adour during the Première Ecole Franco-Espagnole: Groupes de tresses et topologie en petite dimension in October 2009.This is intended to be an introductory survey through which we hope we can briefly outline the power of the concept monodromy as a common area for group theory, algebraic geometry, and topology of projective curves.The main classical results are stated...

Braids and Signatures

Jean-Marc Gambaudo, Étienne Ghys (2005)

Bulletin de la Société Mathématique de France

A braid defines a link which has a signature. This defines a map from the braid group to the integers which is not a homomorphism. We relate the homomorphism defect of this map to Meyer cocycle and Maslov class. We give some information about the global geometry of the gordian metric space.

Braids in Pau – An Introduction

Enrique Artal Bartolo, Vincent Florens (2011)

Annales mathématiques Blaise Pascal

In this work, we describe the historic links between the study of 3 -dimensional manifolds (specially knot theory) and the study of the topology of complex plane curves with a particular attention to the role of braid groups and Alexander-like invariants (torsions, different instances of Alexander polynomials). We finish with detailed computations in an example.

Brunnian links

Paul Gartside, Sina Greenwood (2007)

Fundamenta Mathematicae

A Brunnian link is a set of n linked loops such that every proper sublink is trivial. Simple Brunnian links have a natural algebraic representation. This is used to determine the form, length and number of minimal simple Brunnian links. Braids are used to investigate when two algebraic words represent equivalent simple Brunnian links that differ only in the arrangement of the component loops.

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