For smooth manifolds, the Gysin map of a closed immersion is defined as the cohomology applied on the Pontryagin–Thom collapse map, which collapses the ambient manifold to the one-point compactification of the tubular neighborhood of the closed submanifold. In this talk, I will present a version of the Pontryagin–Thom collapse map in algebraic geometry, more precisely in 𝐏¹-homotopy theory, using a compactified deformation to the normal cone. This yields the Gysin map for all known or unknown cohomology theories with 𝐏¹-homotopy invariance, including étale, Hodge, crystalline, prismatic, etc. I will also survey applications of my Gysin map to more concrete arithmetic questions, including recent work of Carmeli–Feng on Brauer groups of surfaces over finite fields.