On symplectic 4-manifolds with prescribed fundamental group

2005/04/17 by Scott Baldridge, Baldridge, Scott, Paul Kirk +1
Mathematics · #53D05 #57M05 #57R17 #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:53D05 #msc:57M05 #msc:57R17

paper · pdf · doi:10.48550/arxiv.math/0504345

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

openalex publication_date 2005/04/17 · arxiv created 2005/06/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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∈ \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.

Citations

• On Park's exotic smooth four-manifolds
• Symplectic manifolds and their lagrangian submanifolds

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