Branched Covering Constructions and the Symplectic Geography Problem
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Date
2008-08-15T18:09:05Z
Authors
Hughes, Mark Clifford
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
We apply branched covering techniques to construct minimal simply-connected symplectic 4-manifolds with small χ_h values. We also use these constructions to provide an alternate proof that for each s ≥ 0, there exists a positive integer λ(s) such that each pair (j,8j+s) with j ≥ λ(s) is realized as (χ_h(M),c_1^2(M)) for some minimal simply-connected symplectic M. The smallest values of λ(s) currently known to the author are also explicitly computed for
0 ≤ s ≤ 99. Our computations in these cases populate 19 952 points in the (χ,c)-plane not previously realized in the existing literature.
Description
Keywords
4-manifold, branched covering, symplectic geography, symplectic manifold