|
Résumé |
In this talk, I will try to address the question of how to do algebraic topology with stratified spaces and schemes in a meaningful way. I will begin by recalling and motivating some of the main historical attempts to approach this question, both in topology and in algebraic geometry, passing through the work of Nash, Quinn, Siebenmann, Edwards–Hastings, Deligne, and, more recently, Lurie and Barwick–Glasman–Haine. I will then propose my own answer, based on a construction I call the stratified shape.
Time permitting, I will discuss some applications of the stratified shape to proper homotopy theory (joint with Georg Lehner), homology manifolds (joint with Markus Land), and a generalization of Lurie's exodromy equivalence (joint with Peter Haine and Guglielmo Nocera). |
