V. Guillemin

activity

19982005

most citedHow is a graph like a manifold?

16 citations · 40 across the 9 of their papers we have counts for

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8 papers · 1 filter

math.SG2003★ 1 cited

Morse theory on Hamiltonian G-spaces and equivariant K-theory

Victor Guillemin, Mikhail Kogan

Let $G$ be a torus and $M$ a compact Hamiltonian $G$ -manifold with finite fixed point set $M^{G}$ . If $T$ is a circle subgroup of $G$ with $M^{G} = M^{T}$ , the $T$ -moment map is a Morse fu…

math.SG2003★ 5 cited

GKM theory for torus actions with non-isolated fixed points

Victor Guillemin, Tara S. Holm

Let $M^{2 d}$ be a compact symplectic manifold and $T$ a compact $n$ -dimensional torus. A Hamiltonian action, $τ$ , of $T$ on $M$ is a GKM action if, for every $p \in M^{T}$ , the isotr…

math.SG2003★ 1 cited

Potential functions and actions of tori on Kaehler manifolds

D. Burns, V. Guillemin

Let M be a Kaehler manifold with a free, holomorphic and Hamiltonian action of the standard n-torus T. We give a simple, explicit and canonical formula for the Kaehler potential on…

math.SG2001

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…

math.SG2001

The mod 2 cohomology of fixed point sets of anti-symplectic involutions

Daniel Biss, Victor W. Guillemin, Tara S. Holm

Let $M$ be a compact, connected symplectic manifold with a Hamiltonian action of a compact $n$ -dimensional torus $G = T^{n}$ . Suppose that $σ$ is an anti-symplectic involution compatib…

math.SG2001

Symplectic implosion

Victor Guillemin, Lisa Jeffrey, Reyer Sjamaar

Let $K$ be a compact Lie group. We introduce the process of symplectic implosion, which associates to every Hamiltonian $K$ -manifold a stratified space called the imploded cross-se…