Maximal tori in the symplectomorphism groups of Hirzebruch surfaces

TL;DR

This paper counts the conjugacy classes of maximal tori in symplectomorphism groups of certain 4-manifolds, providing insights into their symmetry structures.

Contribution

It introduces a method to classify maximal tori in symplectomorphism groups of specific surfaces, advancing understanding of their group structures.

Findings

Counted conjugacy classes of maximal tori in S^2 x S^2

Counted conjugacy classes in blow-up of CP^2

Provided new classification results for symplectomorphism groups

Abstract

We count the conjugacy classes of maximal tori in the groups of symplectomorphisms of S^2 \times S^2 and of the blow-up of CP^2 at a point.