A Constructive Proof of Alexander Duality

Yann-Situ Gazull (LIS)

Alexander duality refers to a duality theory initiated by a result of J. W. Alexander in 1915, about homology theory properties of the complement of a subspace X in Euclidean space (or a sphere), compared to those of the initial space X. Intuitively, it states that there is a bijection between the holes of an object and the holes of its complement.

In this talk, we will present Alexander duality and give the intuition behind it. We will also present a new constructive proof, obtained using the concept of Homological Discrete Vector Fields (HDVF).