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An Exotic 4-sphere

EasyChair Preprint 9575, version 4

Versions: 1234history
10 pagesDate: August 28, 2023

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.

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, 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

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
@booklet{EasyChair:9575,
  author    = {Valerii Sopin},
  title     = {An Exotic 4-sphere},
  howpublished = {EasyChair Preprint 9575},
  year      = {EasyChair, 2023}}
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