Celebratio Mathematica — Neumann — Complete Bibliography

Complete Bibliography

Works connected to Steven Howard Weintraub

Filter the Bibliography List

year	title	people

			clear

W. D. Neumann and S. H. Weintraub: “Four-manifolds constructed via plumbing,” Math. Ann. 238 : 1 (1978), pp. 71–78. MR 510309 Zbl 0372.57004 article

The following procedure seemed to present a way of constructing interesting 4-manifolds: plumb disc bundles with even euler numbers over 2-spheres together in such a way that the boundary of the resulting 4-manifold \( M_0^4 \) is simply connected, hence \( S^3 \) by von Randow [1962], Scharf [1975], and Montesinos [1975]. Then \( M = M_0^4 \cup D^4 \) is a 4-manifold with even intersection form.

We shall show that the 4-manifolds obtained this way are diffeomorphic to a connected sum of copies of \( S^2\times S^2 \). More generally:

If \( M^4 = M_0^4 \cup D^4 \), where \( M_0^4 \) is a 4-manifold obtained by plumbing with \( \partial M_0 = S^3 \), then either \[ M = (S^2\times S^2)\mathbin{\#}\cdots\mathbin{\#} (S^2\times S^2) \] or \[ M = CP^2 \mathbin{\#}\cdots\mathbin{\#} CP^2 \mathbin{\#}-CP^2\mathbin{\#}\cdots\mathbin{\#}-CP^2 ,\] according as \( M \) has even or odd intersection form.