University of Sydney Algebra Seminar
Nir Gadish
Friday 7 June, 12-1pm, Place: SMRI seminar room (Macleay Building (A12) room 301)
Letter-braiding invariants of words in groups.
How can we tell if a group element can be written as k-fold nested commutator? I suggest seeking computable invariants of words in groups that detect k-fold commutators. We introduce the novel theory of letter-braiding invariants - these are elementarily defined functions on words, inspired by the homotopy theory of loop-spaces and carrying deep geometric content. They give a universal finite-type invariant for arbitrary groups, extending the influential Magnus expansion of free groups that already had countless applications in low dimensional topology. As a consequence we get new combinatorial formulas for braid and link invariants, and a way to linearize automorphisms of general groups that specializes to the Johnson homomorphism of mapping class groups.