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2015

Curve Diagrams, Laminations, and the Geometric Complexity of Braids

Jugé, Vincent

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Braids can be represented geometrically as curve diagrams.

The geometric complexity of a braid is the minimal complexity of a curve diagram representing it.
We introduce and study the corresponding notion of geometric generating function.
We compute explicitly the geometric generating function for the group of braids on three strands and prove that it is neither rational nor algebraic, nor even holonomic.

Curve Diagrams, Laminations, and the Geometric Complexity of Braids · Around

Built on

Theory of braids
Emil Artin · 1947
Earlier work this paper cites.
The braid group and other groups
Frank Garside · 1969
Earlier work this paper cites.
Braids, Links and Mapping Class Groups
Joan Birman · 1974
Earlier work this paper cites.
An Introduction to the Theory of Numbers
Godfrey Hardy and Edward Wright · 1975
Earlier work this paper cites.
Word Processing in Groups
David Epstein, Mike Paterson, James Cannon, Derek Holt, Silvio Levy, and William Thurston · 1992
Earlier work this paper cites.
Geodesic automation and growth functions for artin groups of finite type
Ruth Charney · 1995
Earlier work this paper cites.

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