On symplectic 4-manifolds with prescribed fundamental group

  • Scott Baldridge

    Louisiana State University, Baton Rouge, United States
  • Paul Kirk

    Indiana University, Bloomington, United States

Abstract

In this article we study the problem of minimizing on the class of all symplectic 4-manifolds with prescribed fundamental group ( is the Euler characteristic, is the signature, and ), focusing on the important cases , and . 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 and in terms of the presentation of .

Cite this article

Scott Baldridge, Paul Kirk, On symplectic 4-manifolds with prescribed fundamental group. Comment. Math. Helv. 82 (2007), no. 4, pp. 845–875

DOI 10.4171/CMH/112