## Topology Seminar: Pascal Lambrechts

• Date: 04/12/2012
• Time: 14:00
Lecturer(s):

Pascal Lambrechts

Location:

University of British Columbia

Topic:

From the eversion of the sphere to spaces of knots

Description:

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.

Other Information:

Location: WMAX 216