On symplectic 4-manifolds with prescribed fundamental group

Abstract

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 $G$.

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

References in corpus (2)

• On Park's exotic smooth four-manifolds
• Double node neighborhoods and families of simply connected 4-manifolds with b^+=1

Cited by in corpus (4)

• A symplectic manifold homeomorphic but not diffeomorphic to CP^2 # 3(-CP^2)
• Constructions of small symplectic 4-manifolds using Luttinger surgery
• The geography problem for 4-manifolds with specified fundamental group
• Symplectic 4-manifolds with arbitrary fundamental group near the Bogomolov-Miyaoka-Yau line