C. Zara · wovepaper

activity

19982001

collaborators

6 papers

A GKM description of the equivariant cohomology ring of a homogeneous space

Victor Guillemin, Tara Holm, Catalin Zara

Let $T$ be a torus of dimension $n > 1$ and $M$ a compact $T -$ manifold. $M$ is a GKM manifold if the set of zero dimensional orbits in the orbit space $M / T$ is zero dimensional and t…

Combinatorial formulas for products of Thom classes

Victor Guillemin, Catalin Zara

Let G be a torus of dimension n > 1 and M a compact Hamiltonian G-manifold with $M^{G}$ finite. A circle, $S^{1}$ , in G is generic if $M^{G} = M^{S^{1}}$ . For such a circle the moment map…

G-actions on graphs

Victor Guillemin, Catalin Zara

Let G be an n-dimensional torus and $τ$ a Hamiltonian action of G on a compact symplectic manifold, M. If M is pre-quantizable one can associate with $τ$ a representation of G on a…

Morse theory on graphs

Victor Guillemin, Catalin Zara

Let $Γ$ be a finite d-valent graph and G an n-dimensional torus. An ``action'' of G on $Γ$ is defined by a map, $α$ , which assigns to each oriented edge e of $Γ$ a one-dimensional…

One-skeleta, Betti numbers and equivariant cohomology

Victor Guillemin, Catalin Zara

The one-skeleton of a G-manifold M is the set of points p in M where $dim G_{p} \geq dim G - 1$ ; and M is a GKM manifold if the dimension of this one-skeleton is 2. Goresky, Kottwit…

Equivariant de Rham Theory and Graphs

Victor Guillemin, Catalin Zara

Goresky, Kottwitz and MacPherson have recently shown that the computation of the equivariant cohomology ring of a G-manifold can be reduced to a computation in graph theory. This o…