Miscellaneous papers

[1] Integration of singular braid invariants and graph cohomology,
Transactions of the AMS 350 (1998), 17911809. Postscript PDF
This paper attempts to explain some of the mysteries underlying the
existence of Vassiliev knot invariants from a topological point of
view, in the easier case of braids. In particular we prove necessary
and sufficient conditions for an arbitrary invariant of singular
braids with m double points to be ``integrable'' to a braid invariant.
This gives a slight generalization of the existence theorem for
Vassiliev invariants of braids.

[2] Topological bifurcations of attracting 2tori of
quasiperiodically driven oscillators (with B. Spears and
A. Szeri),
Journal of Nonlinear Science 15 (2005), 423452.
I was a "topology consultant" for this paper, which studies some
knotted 2tori in R^2 x T^2 that arise as attractors in a certain
dynamical system of interest in mechanical engineering. Along the
way, I was surprised to learn that the following seemingly basic
topological question is apparently unsolved: if two closed braids are
isotopic as links in R^2 x S^1, then must they be isotopic through
closed braids? (For braids in R^2 x I, the answer is yes by a
classical theorem of Artin.)
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