Non-holomorphic surface bundles and Lefschetz fibrations

We show how certain stabilizations produce infinitely manyclosed oriented four-manifolds, which are the total spacesof genus $g$ surface bundles (resp. Lefschetz fibrations)over genus $h$ surfaces and have non-zero signature, but donot admit complex structures with either orientations, for“most” (resp. all) possible values of $g \geq 3$ and $h\geq 2$ (resp. $g \geq 2$ and $h \geq 0$).

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Published 8 November 2012