## Topology Seminar: Pascal Lambrechts

- Date: 04/12/2012
- Time: 14:00

Pascal Lambrechts

University of British Columbia

From the eversion of the sphere to spaces of knots

Abstract

A famous result by Steven Smale states that we can turn the sphere

inside-out through immersions: this is called the eversion of the

sphere. We will explain this result and the strategy of its proof which

is a "cut-and-paste" strategy quite standard in algebraic topology. This

approach allows us to understand globally the space of all immersions

of a given manifold in another one, like the space of all immersion of

the sphere in R^3 in the case of Smale's eversion. This theory has been

enhanced by Goodwillie in the 1990's to understand spaces of embeddings.

We will explain how this can be applied to understand spaces of knots,

that is the spaces of all embeddings of a circle into a fixed euclidean

space.