Classification of closed oriented 4-manifolds modulo connected sum with simply connected manifolds
نویسندگان
چکیده
منابع مشابه
On Simply-connected 4-manifolds
This paper concerns (but does not succeed in performing) the diffeomorphism classification of closed, oriented, differential, simply-connected 4-manifolds. It arises out of the observation (due to Pontrjagin and Milnor [2]) that if two such manifolds Mx and M2 have isomorphic quadratic forms of intersection numbers on #2(Jft-), then there is a map / : M1-^-Mi which is a homotopy equivalence and...
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In this article we construct a new family of simply connected symplectic 4-manifolds with b+2 = 1 and c 2 1 = 2 which are not diffeomorphic to rational surfaces by using rational blow-down technique. As a corollary, we conclude that a rational surface CP ♯7CP 2 admits an exotic smooth structure.
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Hitchin proved that if M is a spin manifold with positive scalar curvature, then the A^O-characteristic number a(M) vanishes. Gromov and Lawson conjectured that for a simply connected spin manifold M of dimension > 5, the vanishing of a(M) is sufficient for the existence of a Riemannian metric on M with positive scalar curvature. We prove this conjecture using techniques from stable homotopy th...
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Introduction and the Statement. In [A] S. Akbulut obtained an example of the exotic manifold cutting off the contractible submanifold from the standard manifold and regluing it via nontrivial involution of the boundary. In these notes we give a proof of a decomposition theorem stated below. It generalizes the example of Akbulut. Another proof of the theorem was independently obtained by C.L. Cu...
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ژورنال
عنوان ژورنال: Hiroshima Mathematical Journal
سال: 1998
ISSN: 0018-2079
DOI: 10.32917/hmj/1206126759