| DATE: | Thursday, November 16, 2000 |
| TIME: | 4:30-5:30 PM |
| PLACE: | LN 2205 |
| SPEAKER: | Peter Linnell, Virginia Tech |
| TITLE: | Left ordered groups |
A group G is left ordered if it has a total ordering (that is a
relation <= such that for all f,g,h in G,
f <= f
f <= g and g <= f implies f = g, and
f <= g <= h implies f <= h)
which is left invariant (that is f <= h implies gf <= gh).
An example of a left ordered group is the real numbers under addition
with the usual order. Left ordered groups can be studied in a
very algebraic way.
On the other hand it can be shown that any countable left ordered
group is isomorphic to a subgroup of Aut(R), the group of orientation
preserving homeomorphisms of the real line. This means that left
ordered groups can be studied in an analytic way. One can use this
point of view to prove that Braid groups are left ordered.
In this talk, I will discuss these two approaches. This talk should
be accessible to graduate students.