Everyone welcome. Refreshments will be served in the Math Lounge before the exam.

**Friday, May 18, 2012, 2:10 p.m., in BA 6183, 40 St. George Street **

**PhD Candidate**: Karene Chu ** **

**PhD Advisor**: Dror Bar-Natan

**Thesis Title**: Flat Virtual Pure Tangles (http://www.math.toronto.edu/karene/Thesis120509.pdf)

**Thesis Abstract**:

Virtual knot theory, introduced by Kauffman, is a generalization of classical knot theory which interests us because its finite-type invariant theory is potentially a topological interpretation of Etingof and Kazhdan’s theory of quantization of Lie bialgebras. Classical knots inject into virtual knots, and flat virtual knots is the quotient of virtual knots which equates the real positive and negative crossings, and in this sense is complementary to classical knot theory within virtual knot theory.

We classify flat virtual tangles with no closed components and give bases for its “infinitesimal” algebras. As a corollary, we also obtain a classification of free virtual tangles with no closed components. The classification of the former can be used as an invariant on virtual pure tangles. In a subsequent paper, we will show that the infinitesimal algebras are indeed the target spaces of any universal finite-type invariants on the respective variants of flat virtual tangles.

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