On Nash's 4-sphere and Property 2R

Motoo Tange

On Nash's 4-sphere and Property 2R

Geometric Topology 2011-02-17 v1

Authors: Motoo Tange

Abstract

D.Nash defined a family of homotopy 4-spheres in [11]. Proving that his manifolds ${\mathcal S}_{m,n,m',n'}$ are all real $S^4$ , we find that they have handle decomposition with no 1-handles, two 2-handles and two 3-handles. The handle structures give new potential counterexamples of Property 2R conjecture.

Cite

@article{arxiv.1102.3207,
  title  = {On Nash's 4-sphere and Property 2R},
  author = {Motoo Tange},
  journal= {arXiv preprint arXiv:1102.3207},
  year   = {2011}
}

Comments

19 pages, 39 figures

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