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From Christoffel words to braids

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From Christoffel words to braids Christian Kassel Institut de Recherche Mathématique Avancée CNRS - Université Louis Pasteur Strasbourg, France Colloquium at Rutgers 13 April 2007

  • matematica pura ed

  • group f2

  • annali di

  • finite words

  • planar geometry

  • joint work


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Nombre de lectures

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Kassel Louis Pasteur University Institut de recherche mathématique avancée
From Christoffel words to braids
Christian Kassel
Institut de Recherche Mathématique Avancée CNRS  Université Louis Pasteur Strasbourg, France
Colloquium at Rutgers 13 April 2007
Joint work
•WithChristophe Reutenauer, UQAM, Montréal, Canada
•Paper published in Annali di Matematica Pura ed Applicata186 (2007), 317–339 Downloadable from arXiv:math.GR/0507219
What is it about?
Construct words from simple planar geometry ◮
◮ Words on two letters Christoffel words:finite words ◮ ◮ Sturmian sequences:infinite words
In relation to ◮ bases of the free groupF2on two generators ◮ ◮ the braid groupB4on four strands
What is it about?
Construct words from simple planar geometry ◮
Words on two letters ◮ Christoffel words:finite words ◮ ◮ Sturmian sequences:infinite words
◮ In relation to bases of the free groupF2on two generators ◮ the braid groupB4on four strands ◮
What is it about?
Construct words from simple planar geometry ◮
Words on two letters ◮ ◮ Christoffel words:finite words Sturmian sequences:infinite words ◮
◮ In relation to ◮ bases of the free groupF2on two generators ◮ the braid groupB4on four strands
What is it about?
Construct words from simple planar geometry ◮
◮ Words on two letters ◮ Christoffel words:finite words ◮ Sturmian sequences:infinite words
◮ In relation to bases of the free groupF2on two generators ◮ ◮ the braid groupB4on four strands
What is it about?
Construct words from simple planar geometry ◮
Words on two letters ◮ Christoffel words:finite words ◮ Sturmian sequences:infinite words ◮
◮ In relation to ◮ bases of the free groupF2on two generators ◮ the braid groupB4on four strands
What is it about?
◮ Construct words from simple planar geometry
Words on two letters ◮ Christoffel words:finite words ◮ ◮ Sturmian sequences:infinite words
◮ In relation to ◮ bases of the free groupF2on two generators the braid groupB4on four strands ◮
What is it about?
◮ Construct words from simple planar geometry
◮ Words on two letters ◮ Christoffel words:finite words ◮ Sturmian sequences:infinite words
◮ In relation to ◮ bases of the free groupF2on two generators ◮ the braid groupB4on four strands
I. HISTORICAL BACKGROUND
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