Some properties of a conjugation-free geometric presentation of fundamental groups of arrangements
speaker: David Garber (Department of Applied Mathematics, Holon Institute of Technology,)abstract:
A conjugation-free geometric presentation of a fundamental group is a presentation with the natural topological generators x1 , … , xn and the cyclic relations:
xik xik−1 ⋯ xi1 = xik−1 ⋯ xi1 xik = ⋯ = xi1 xik ⋯ xi2
with no conjugations on the generators. We study some properties of this type of presentations for a fundamental group of a line arrangement’s complement. We actually show that a large family of these presentations satisfy a completeness property in the sense of Dehornoy. The completeness property is a powerful property which leads to many nice properties concerning the presentation (as the left-cancellativity in the associated monoid and yields some simple criterion for the solvability of the word problem in the group). Joint work with Meital Eliyahu and Mina Teicher.
timetable:
Tue 22 Jun, 17:30 - 18:00, Aula Dini
documents:
Garber
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