Coarse separation of Euclidean spaces

Abstract: A subspace $S$ of a topological space $X$ is said to separate if $X - S$ contains more than one path-component. The classical Alexander duality theorem implies that if a subset $A$ of the $n$-dimensional sphere separates it, then $A$ must be of (topological) dimension $n - 1$. Coarse separation is an analogue of topological separation in the world of metric spaces. Coarse separation arises naturally in geometric group theory. I will introduce asymptotic dimension which is an analogue of topological dimension in the coarse setting. It was conjectured that every coarsely separating subset of $\mathbb{R}^n$ is of asymptotic dimension at least $n-1$. I have proved this conjecture. I will give an outline of the proof of this result.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.