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Free Differential Calculus
Student-Run Research Seminar| Speaker: | Mike Williams, UC Davis |
| Location: | 693 Kerr |
| Start time: | Wed, Oct 26 2005, 12:10PM |
The free differential calculus is a tool for studying finitely presented groups, especially knot groups. If G is a finitely presented group < S|R >, then one defines partial derivatives with respect to each generator from S. The derivatives have "values" in the group ring Z[G]. If G is a free group on n-generators, then these derivatives have a simple "geometric" interpretation as an unraveling of loops from an n-leaved rose to an "infinite snowflake". Topologically speaking, G is the fundamental group of the n-leaved rose, and the derivatives give lifts of elements of G to the universal cover. My presentation will be based on writings of R.H. Fox and L.H. Kauffman.