Branched Covering Constructions and the Symplectic Geography Problem

4-manifold;branched covering;symplectic geography;symplectic manifold;Pure Mathematics

Hughes, Mark Clifford

University of Waterloo

关键词: 4-manifold;    branched covering;    symplectic geography;    symplectic manifold;    Pure Mathematics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/3857/1/BranchedSymplectic.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

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 computedfor 0 ≤ s ≤ 99.Our computations in these cases populate 19 952 points in the (χ,c)-plane not previously realized in the existing literature.