EVENT DETAILS AND ABSTRACT

Title: Stable homotopy theory and geometry
Speaker: Paul VanKoughnett
Speaker Info:
Brief Description:
Special Note:
Abstract:

The homotopy groups of spheres form an intricate algebraic structure whose calculation has been a major area of research in topology over the last century. While the question of how spheres can be mapped into one another is tantalizing in its own right, it also throws surprising light on questions in manifold geometry, like how manifolds can be embedded in Euclidean space and when manifolds admit differentiable structures. I'll define the homotopy groups of spheres and begin to describe their calculation, emphasizing their relationship with geometry.