Generalized complex hamiltonian torus actions: Examples and constraints

TL;DR

This paper investigates Hamiltonian torus actions on generalized complex manifolds, establishing rank constraints and constructing new examples with maximal rank using surgery techniques, while analyzing the persistence of topological twisting under reduction.

Contribution

It proves rank bounds for torus actions on generalized complex manifolds and introduces a surgery method to construct new examples with maximal rank.

Findings

Rank(T) q n-2 for effective Hamiltonian torus actions.

Topological twisting persists after Hamiltonian reduction.

Constructed new examples of actions with rank(T) = n-2 using surgery.

Abstract

Consider an effective Hamiltonian torus action $T\times M \to M$ on a topologically twisted,generalized complex manifold $M$ of dimension $2n$. We prove that the $rank(T) \leq n-2$ and that the topological twisting survives Hamiltonian reduction. We then construct a large new class of such actions satisfying $rank(T) = n-2$, using a surgery procedure on toric manifolds.