##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry

## Guofang Wei

#### UC Santa Barbara

## The covering spectrum of a compact length space

##### Abstract:

We define a new spectrum for compact length spaces and Riemannian manifolds called the ``covering spectrum" which roughly measures the size of the one dimensional holes in the space. More specifically, the covering spectrum is a set of real numbers $\delta>0$ which identify the distinct $\delta$ covers of the space. We investigate the relationship between this covering spectrum, the length spectrum, the marked length spectrum and the Laplace spectrum. We analyze the behavior of the covering spectrum under Gromov-Hausdorff convergence. This is a joint work with C. Sormani.

Host: Lei Ni

### November 10, 2004

### 3:00 PM

### AP&M 7218

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