Speaker:
Title:
Abstract: A Brunnian link is a link of simple closed curves in three-space which
can be untangled after any single curve is deleted. A Brunnian
braid is a braid which becomes trivial with the deletion of any single
strand. A Brunnian word in the free group on n symbols is a
word which reduces to the identity when all the occurrences of any single
symbol are deleted from it. (I will give more precise definitions in my talk.)
I will give several constructions of Brunnian links, and then I will show that
Brunnian braids and free group elements, which are defined combinatorially
or geometrically, can be completely characterized algebraically via a sort
of commutator collection process.
I may also talk about Brunnian graphs, which are knotted graphs in three-space
which become topologically planar when any single edge is deleted. And I may
talk about n-triviality, which is a property closely related to "Brunnian", but
which was defined much more recently and is related to quantum knot theory.