On symplectic 4-manifolds with prescribed fundamental group

Details On symplectic 4-manifolds with prescribed fundamental group On symplectic 4-manifolds with prescribed fundamental group

2005-04-17

arxiv.org/abs/math/0504345v3

Mathematics

Geometric Topology

30 pages, 4 figures. New Version: Added examples covering free abelian groups with odd rank

Scientific paper

In this article we study the problem of minimizing $a\chi+b\sigma$ on the class of all symplectic 4--manifolds with prescribed fundamental group $G$ ($\chi$ is the Euler characteristic, $\sigma$ is the signature, and $a,b\in \BR$), focusing on the important cases $\chi$, $\chi+\sigma$ and $2\chi+3\sigma$. In certain situations we can derive lower bounds for these functions and describe symplectic 4-manifolds which are minimizers. We derive an upper bound for the minimum of $\chi$ and $\chi+\sigma$ in terms of the presentation of $G$.

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