The geometry of the Bing involution


70 years ago Bing produced a wild involution of the three-sphere bringing a technique “decomposition space theory” to life. This technique was later crucial in the solutions to both the double suspension problem and the 4D Poincare conjecture.  Mike Starbird and I have recently completed a 40 year project to understand the modulus of continuity of Bing’s involution (considered as a conjugacy class –  that is in general coordinates): it is indeed very wild!