Open AccessOn Nash\'s 4-sphere and Property 2R
Author(s) -
Motoo Tange
Publication year - 2013
Publication title -
turkish journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.454
H-Index - 27
eISSN - 1303-6149
pISSN - 1300-0098
DOI - 10.3906/mat-1104-1
Subject(s) - mathematics , property (philosophy) , counterexample , conjecture , homotopy , nash equilibrium , decomposition , pure mathematics , combinatorics , discrete mathematics , mathematical economics , ecology , philosophy , epistemology , biology
D. Nash defined a family of homotopy 4-spheres in (11). Proving that his manifolds Sm,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.
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