A conjugation-free geometric presentation of fundamental groups of arrangements II: Expansion and some properties

Details A conjugation-free geometric presentation of fundamental groups of arrangements II: Expansion and some properties A conjugation-free geometric presentation of fundamental groups of arrangements II: Expansion and some properties

2010-09-07

arxiv.org/abs/1009.1349v1

Mathematics

Geometric Topology

20 pages, 12 figures; submitted

Scientific paper

A conjugation-free geometric presentation of a fundamental group is a presentation with the natural topological generators $x_1, \dots, x_n$ and the cyclic relations: $x_{i_k}x_{i_{k-1}} \cdots x_{i_1} = x_{i_{k-1}} \cdots x_{i_1} x_{i_k} = \cdots = x_{i_1} x_{i_k} \cdots x_{i_2}$ with no conjugations on the generators. We have already proved that if the graph of the arrangement is a disjoint union of cycles, then its fundamental group has a conjugation-free geometric presentation. In this paper, we extend this property to arrangements whose graphs are a disjoint union of cycle-tree graphs. Moreover, we study some properties of this type of presentations for a fundamental group of a line arrangement's complement. We show that these presentations satisfy a completeness property in the sense of Dehornoy, if the corresponding graph of the arrangement is triangle-free. The completeness property is a powerful property which leads to many nice properties concerning the presentation (as the left-cancellativity of the associated monoid and yields some simple criterion for the solvability of the word problem in the group).

Affiliated with

Also associated with

No associations

Rating

A conjugation-free geometric presentation of fundamental groups of arrangements II: Expansion and some properties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A conjugation-free geometric presentation of fundamental groups of arrangements II: Expansion and some properties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A conjugation-free geometric presentation of fundamental groups of arrangements II: Expansion and some properties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-704929