On the conformal systoles of four-manifolds

Abstract

We extend a result of M. Katz on conformal systoles to all four-manifolds with b^+=1 which have odd intersection form. The same result holds for all four-manifolds with b^+=1 with even intersection form and which are symplectic or satisfy the so-called 5/4-conjecture.

6 pages, revised version; relation of main result to type of intersection form, symplectic structures and the 5/4-conjecture clarified; to appear in manuscripta mathematica

References in corpus (2)

• Singular Lefschetz pencils
• Constructing symplectic forms on 4-manifolds which vanish on circles

Cited by in corpus (2)

• Logarithmic growth of systole of arithmetic Riemann surfaces along congruence subgroups
• On manifolds satisfying stable systolic inequalities