Download PDFOpen PDF in browser

An Exotic 4-sphere

EasyChair Preprint no. 9575, version 4

Versions: 1234history
10 pagesDate: August 28, 2023


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.

This paper is a survey of recent advances towards the last generalized Poincare conjecture (connections with Berkovich analytic spaces, the Richter-Gebert’s Universality theorem and cluster algebras are presented) with some approaches to the resulting solution.

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

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
  author = {Valerii Sopin},
  title = {An Exotic 4-sphere},
  howpublished = {EasyChair Preprint no. 9575},

  year = {EasyChair, 2023}}
Download PDFOpen PDF in browser