##### Department of Mathematics,

University of California San Diego

****************************

### Math 295 - Mathematics Colloquium

## Ezra Getlzer

#### Northwestern University

## n-groups

##### Abstract:

In this talk, we give a brief introduction to a natural generalization of groups, called n-groups.\\ Just as discrete groups represent the homotopy types of acyclic spaces, n-groups realize homotopy types of connected topological spaces $X$ such that $\pi_i(X)=0$ for $i>n$. In this talk, we adopt the formalism of simplicial sets, and define n-groups as simplicial sets satisfying certain a filling condition (introduced by Duskin).\\ In the first part of the talk, we explain what a 2-group look like: this material is contained in any textbook on simplicial sets. We indicate how 2-groups arise in topological quantum field theory.

Host: Ben Weinkove

### March 11, 2009

### 4:00 PM

### AP&M 6402

****************************