34 citations · 91 across the 28 of their papers we have counts for
23 papers · 1 filter
Four-periodic infinite staircases for four-dimensional polydisks
Caden Farley, Tara Holm, Nicki Magill +4
The ellipsoid embedding function of a symplectic four-manifold measures the amount by which its symplectic form must be scaled in order for it to admit an embedding of an ellipsoid…
Infinite staircases for Hirzebruch surfaces
Maria Bertozzi, Tara S. Holm, Emily Maw +4
We consider the embedding capacity functions for symplectic embeddings of ellipsoids of eccentricity into the family of nontrivial rational Hirzebruch surfaces $H_…
On infinite staircases in toric symplectic four-manifolds
Dan Cristofaro-Gardiner, Tara S. Holm, Alessia Mandini +1
An influential result of McDuff and Schlenk asserts that the function that encodes when a four-dimensional symplectic ellipsoid can be embedded into a four-dimensional ball has a r…
Equivariant cohomology of a complexity-one four-manifold is determined by combinatorial data
Tara Holm, Liat Kessler
For Hamiltonian circle actions on compact, connected, four-dimensional manifolds, we give a generators and relations description for the even part of the equivariant cohomology, as…
The equivariant cohomology of complexity one spaces
Tara S. Holm, Liat Kessler
Complexity one spaces are an important class of examples in symplectic geometry. Karshon and Tolman classify them in terms of combinatorial and topological data. In this paper, we…
Circle actions on symplectic four-manifolds
Tara S. Holm, Liat Kessler
We complete the classification of Hamiltonian torus and circle actions on symplectic four-dimensional manifolds. Following work of Delzant and Karshon, Hamiltonian circle and 2-tor…
The fundamental group and Betti numbers of toric origami manifolds
Tara S. Holm, Ana Rita Pires
Toric origami manifolds are characterized by origami templates, which are combinatorial models built by gluing polytopes together along facets. In this paper, we examine the topolo…
The Morse-Bott-Kirwan condition is local
Tara Holm, Yael Karshon
Kirwan identified a condition on a smooth function under which the usual techniques of Morse-Bott theory can be applied to this function. We prove that if a function satisfies this…
The topology of toric origami manifolds
Tara Holm, Ana Rita Pires
A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami…
Simple Hamiltonian manifolds
Jean-Claude Hausmann, Tara S. Holm
A simple Hamiltonian manifold is a closed connected symplectic manifold equipped with a Hamiltonian action of a torus T with moment map Phi: M-->t^*, such that the fixed set M^T ha…
Equivariant cohomology for Hamiltonian torus actions on symplectic orbifolds
Tara Holm, Tomoo Matsumura
In this paper, we study Hamiltonian R-actions on symplectic orbifolds [M/S], where R and S are tori. We prove an injectivity theorem and generalize Tolman-Weitsman's proof of the G…
Torsion in the full orbifold K-theory of abelian symplectic quotients
Rebecca Goldin, Megumi Harada, Tara S. Holm
Let (M,ω,Φ) be a Hamiltonian T-space and let H be a closed Lie subtorus of T. Under some technical hypotheses on the moment map Φ, we prove that there is no additive torsion in the…
The Full Orbifold -theory of Abelian Symplectic Quotients
Rebecca Goldin, Megumi Harada, Tara S. Holm +1
In their 2007 paper, Jarvis, Kaufmann, and Kimura defined the full orbifold -theory of an orbifold , analogous to the Chen-Ruan orbifold cohomology of ${\mathfrak…
Act globally, compute locally: group actions, fixed points, and localization
Tara S. Holm
Localization is a topological technique that allows us to make global equivariant computations in terms of local data at the fixed points. For example, we may compute a global inte…
Orbifold cohomology of abelian symplectic reductions and the case of weighted projective spaces
Tara S. Holm
These notes accompany a lecture about the topology of symplectic (and other) quotients. The aim is two-fold: first to advertise the ease of computation in the symplectic category;…
Connectivity properties of moment maps on based loop groups
Megumi Harada, Tara S Holm, Lisa C Jeffrey +1
For a compact, connected, simply-connected Lie group G, the loop group LG is the infinite-dimensional Hilbert Lie group consisting of H^1-Sobolev maps S^1-->G. The geometry of LG a…
Orbifold cohomology of torus quotients
Rebecca Goldin, Tara S. Holm, Allen Knutson
We introduce the_inertial cohomology ring_ NH^*_T(Y) of a stably almost complex manifold carrying an action of a torus T. We show that in the case that Y has a locally free action…
GKM theory for torus actions with non-isolated fixed points
Victor Guillemin, Tara S. Holm
Let be a compact symplectic manifold and a compact -dimensional torus. A Hamiltonian action, , of on is a GKM action if, for every , the isotr…
Distinguishing the Chambers of the Moment Polytope
Rebecca F. Goldin, Tara S. Holm, Lisa C. Jeffrey
Let M be a compact manifold with a Hamiltonian T action and moment map Phi. The restriction map in equivariant cohomology from M to a level set Phi^{-1}(p) is a surjection, and we…
Real loci of symplectic reductions
R. F. Goldin, T. S. Holm
Let be a compact, connected symplectic manifold with a Hamiltonian action of a compact -dimensional torus . Suppose that is equipped with an anti-symplectic involutio…
A GKM description of the equivariant cohomology ring of a homogeneous space
Victor Guillemin, Tara Holm, Catalin Zara
Let be a torus of dimension and a compact manifold. is a GKM manifold if the set of zero dimensional orbits in the orbit space is zero dimensional and t…
The equivariant cohomology of Hamiltonian -spaces From Residual Actions
Rebecca Goldin, Tara S. Holm
We show that for a Hamiltonian action of a compact torus on a compact, connected symplectic manifold , the -equivariant cohomology is determined by the residual act…
The mod 2 cohomology of fixed point sets of anti-symplectic involutions
Daniel Biss, Victor W. Guillemin, Tara S. Holm
Let be a compact, connected symplectic manifold with a Hamiltonian action of a compact -dimensional torus . Suppose that is an anti-symplectic involution compatib…