Leonor Godinho

Blowing Up Symplectic Orbifolds

In the first part of this paper we study different blow-upconstructions on symplectic orbifolds. Unlike the manifold case,we can define different blow-ups by using different circleactions. In the second part, we use some of these constructions todescribe the behavior of reduced spaces of a Hamiltonian circleaction on a symplectic orbifold, when passing a critical level ofits Hamiltonian function. Using these descriptions, we generalize,in the manifold case, the wall-crossing theorem of Guillemin and Sternberg to the case of a Hamiltonian torus action not necessarily quasi-free and also the Duistermaat–Heckman theorem to intervalsof values of the Hamiltonian function containing critical values.

New Tools for Classifying Hamiltonian Circle Actions with Isolated Fixed Points

For every compact almost complex manifold

Equivariant Cohomology of S 1 -Actions on 4-Manifolds

(\mathsf {M},\mathsf {J})

4

(M,J) equipped with a

THE FUNDAMENTAL GROUP OF S 1 -MANIFOLDS

\mathsf {J}

Addendum and Erratum to "The Fundamental Group of

J-preserving circle action with isolated fixed points, a simple algebraic identity involving the first Chern class is derived. This enables us to construct an algorithm to obtain linear relations among the isotropy weights at the fixed points. Suppose that