Topology Seminar: Pascal Lambrechts
Topic
From the eversion of the sphere to spaces of knots
Speakers
Details
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.
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.
