An Exotic 4-sphere

EasyChair Preprint 9575, version 1

Abstract

It has not been known whether or not there are any exotic 4-spheres: such an exotic 4-sphere would be a counterexample to the smooth generalized Poincare conjecture in dimension 4. Some plausible candidates are given by Gluck twists, but many cases over the years were ruled out as possible counterexamples. In the paper the resulting solution to the last generalized Poincare conjecture is presented by giving a precise construction of a discrete exotic 4-sphere (Berkovich analytic spaces and the Richter-Gebert’s Universality theorem help).

Keyphrases: Berkovich analytic spaces, Exotic n-spheres, Exotic smooth structures, Pachner moves, Piecewise-linear manifolds, Poincare conjecture, Rado graph, Richter-Gebert’s Universality theorem, Subdivisions, Valuation, Weighted simplicial complexes, discrete geometry, inverse limit, simplicial complexes, triangulations

@booklet{EasyChair:9575,
  author    = {Valerii Sopin},
  title     = {An Exotic 4-sphere},
  howpublished = {EasyChair Preprint 9575},
  year      = {EasyChair, 2023}}