Geodesic
A Note on Doubles of 4-Manifolds
Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 367-369

Voir la notice de l'article provenant de la source Cambridge University Press

If M is a simply-connected 4-manifold with boundary, let D(M) denote its double MU ∂M (-M). If M is closed, let D(M) denote M#-M. In either case, D(M) is a simply-connected 4-manifold of index zero, and so by a theorem of Wall [8], M#k(S 2xS 2) must be standard for k sufficiently large, where by standard we mean diffeomorphic to the connected sum of copies of S 2 x S 2 and S 2×S 2, the non-trivial S 2 bundle over S 2 (which is itself diffeomorphic to CP2#-CP2 [7]). In this paper we give abound on k, in the case where M has no 3-handles. 
Weintraub, Steven H. A Note on Doubles of 4-Manifolds. Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 367-369. doi: 10.4153/CMB-1980-053-x
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