High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible. The post In the ‘Wild West’ of Geometry, Mathematicians Redefine the Sphere first appeared on Quanta Magazine
If you’ve ever been stuck in traffic on a rainy afternoon, you’ve probably watched raindrops racing each other down the car window. When pairs of droplets collide, they merge into a new droplet, losing their separate identities. That merging is possible because the water droplets are just about spherical. When shapes are flexible — as raindrops are — attaching a sphere doesn’t change anything.