Intersection Forms of Spin Four-manifolds
نویسنده
چکیده
Furuta in [19] had obtained an estimate b (X) ≥ 2+ 10 8 ·|signature (X) | for spin manifolds with arbitrary fundamental groups and nonzero signature. The main theorem 2.1 in this note generalizes Furuta’s 10/8-theorem to the case of spin four-manifolds bounding disjoint unions of rational homology spheres. Theorem 1.1 is deduced from this generalized 10/8-theorem. To get an idea, how this comes about, note the extra summand 2 in the statement of the 10 8 -theorem. Suppose a closed four-manifold is cut into pieces along embedded homology spheres. Then every piece carrying nonzero signature
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