On Nash\'s 4-sphere and Property 2R

Authors: MOTOO TANGE

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

Keywords: Homotopy 4-spheres, Property 2R, handle calculus

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