Subject: A braid group question for the topology list Date: Mon, 21 Jun 2004 12:18:48 -0500 From: David Yetter Has anyone encountered the following subgroups of Artin's braid groups before: The subgroup of all pure braids such that the all linking numbers of the link obtained by closing the braid are all zero? These are not the Brunnian braids: for n = 2 all pure braids are Brunnian, for n = 3 the two subgroups coincide, for n > 3 the subgroup I'm looking for is larger, as it contains all tensor products of Brunnian braids (for instance at n = 6 the tensor product of two copies of a 3-braid B which represents the Borromean rings, or for that matter at n = 4 it contains 1\otimes B, B\otimes 1, and their product, none of which is Brunnian. Best regards to all, David Yetter Assoc. Prof. of Mathematics Kansas State University