##### Department of Mathematics,

University of California San Diego

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### Math 292 - Topology Seminar

## Jim Conant

#### UCSD

## Tensor powers of Hopf algebras and the Johnson Homomorphism

##### Abstract:

The (higher order) Johnson homomorphism embeds the associated graded Lie algebra for the mapping class group of a once punctured surface into a certain Lie algebra. Calculating the image of the Johnson homomorphism is a challenging problem. Shigeyuki Morita was the first to define obstructions to lying in the image back in the 90s. More recently Enomoto and Satoh have defined a new series of obstructions, and work of Conant-Kassabov-Vogtmann has provided a rich family of obstructions, involving classical modular forms, stemming from the abelianization of the target Lie algebra. In this talk, I will present joint work with Martin Kassabov which simultaneously generalizes all of these obstructions, making use of an apparently new action of $Aut(F_n) on H^{\otimes n}$ for any cocommutative Hopf algebra H.

Host: Justin Roberts

### April 8, 2014

### 10:30 AM

### AP&M 7218

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