On symplectic 4-manifolds with prescribed fundamental group

Scott Baldridge; Paul Kirk

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On symplectic 4-manifolds with prescribed fundamental group

Scott Baldridge·Paul Kirk

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Abstract

In this article we study the problem of minimizing $aχ+bσ$ on the class of all symplectic 4--manifolds with prescribed fundamental group $G$ ($χ$ is the Euler characteristic, $σ$ is the signature, and $a,b\in \BR$), focusing on the important cases $χ$, $χ+σ$ and $2χ+3σ$. 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 $χ$ and $χ+σ$ in terms of the presentation of $G$.

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BibTeX RIS

Scott Baldridge, Paul Kirk. 2005-06-07. On symplectic 4-manifolds with prescribed fundamental group. https://arxiv.org/abs/math/0504345

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