5 citations · 8 across the 19 of their papers we have counts for
21 papers
On orientability, Poincaré duality, and connectivity of GKM graphs
Oliver Goertsches, Panagiotis Konstantis, Leopold Zoller
We investigate a combinatorial notion of orientability for abstract GKM graphs and its connections to graph cohomology in the sense of Guillemin--Zara. In particular, we prove that…
Finiteness and boundedness of positive monotone Hamiltonian GKM spaces
Panagiotis Konstantis, Silvia Sabatini, Leopold Zoller
In this paper, we establish three finiteness and boundedness theorems for compact positive monotone symplectic manifolds endowed with special actions, called GKM, which general…
Strong formality of toric and homogeneous compact Kähler manifolds
Giovanni Placini, Jonas Stelzig, Leopold Zoller
All compact Kähler, or even -manifolds, are rationally formal. Not all of them are strongly formal. Yet some of them are: For complete smooth complex toric va…
On torus equivariant -bundles over and Petrie-type questions for GKM manifolds
Oliver Goertsches, Panagiotis Konstantis, Leopold Zoller
We classify -GKM fibrations in which both fiber and base are the GKM graph of , with standard weights in the base. For each case in which the total space is orientable, w…
On GKM fiber bundles and realizability with full flag fibers
Oliver Goertsches, Panagiotis Konstantis, Nikolas Wardenski +1
We investigate under which conditions an equivariant fiber bundle whose base, total space and fiber are GKM manifolds induces a fibration or fiber bundle of the corresponding GKM g…
On integral Chang-Skjelbred computations with disconnected isotropy groups
Leopold Zoller
The Chang-Skjelbred method computes the cohomology of a suitable space with a torus action from its equivariant one-skeleton. We show that, under certain restrictions on the cohomo…
Nontrivial Massey products on compact Kähler manifolds
Giovanni Placini, Jonas Stelzig, Leopold Zoller
We show that the bigraded quasi-isomorphism type of the bigraded, bidifferential algebra of forms on a compact Kähler manifold generally contains more information than the de Rham…
On the Stiefel-Whitney classes of GKM manifolds
Oliver Goertsches, Panagiotis Konstantis, Leopold Zoller
We show that under standard assumptions on the isotropy groups of an integer GKM manifold, the equivariant Stiefel-Whitney classes of the action are determined by the GKM graph. Th…
Formality is preserved under domination
Aleksandar Milivojevic, Jonas Stelzig, Leopold Zoller
If a closed orientable manifold (resp. rational Poincaré duality space) receives a map from a formal manifold (resp. space) that hits a fundamental class, then $X…
Low-dimensional GKM theory
Oliver Goertsches, Panagiotis Konstantis, Leopold Zoller
GKM theory is a powerful tool in equivariant topology and geometry that can be used to generalize classical ideas from (quasi)toric manifolds to more general torus actions. After a…
The GKM correspondence in dimension 6
Oliver Goertsches, Panagiotis Konstantis, Leopold Zoller
It follows from the GKM description of equivariant cohomology that the GKM graph of a GKM manifold has free equivariant graph cohomology, and satisfies a Poincaré duality condition…
Poincaré dualization and Massey products
Aleksandar Milivojevic, Jonas Stelzig, Leopold Zoller
We study the rational homotopy theoretic and geometric properties of a construction which extends any cohomologically connected, finite type cdga to one satisfying cohomological Po…
Torus equivariant algebraic models and compact realization
Leopold Zoller
Let be a compact torus. We prove that, up to equivariant rational equivalence, the category of -simply connected, -finite type -spaces with finitely many isotropy type…
Reconstructing the orbit type stratification of a torus action from its equivariant cohomology
Oliver Goertsches, Leopold Zoller
We investigate what information on the orbit type stratification of a torus action on a compact space is contained in its rational equivariant cohomology algebra. Regarding the (la…
GKM manifolds are not rigid
Oliver Goertsches, Panagiotis Konstantis, Leopold Zoller
We construct effective GKM -actions with connected stabilizers on the total spaces of the two -bundles over with identical GKM graphs. This shows that the GKM graph…
Realization of GKM fibrations and new examples of Hamiltonian non-Kähler actions
Oliver Goertsches, Panagiotis Konstantis, Leopold Zoller
We classify fibrations of abstract -regular GKM graphs over -regular ones, and show that all fiberwise signed fibrations of this type are realized as the projectivization of…
The Toral Rank Conjecture and variants of equivariant formality
Manuel Amann, Leopold Zoller
An action of a compact Lie group is called equivariantly formal, if the Leray--Serre spectral sequence of its Borel fibration degenerates at the E_2-term. This term is as prominent…
GKM theory and Hamiltonian non-Kähler actions in dimension
Oliver Goertsches, Panagiotis Konstantis, Leopold Zoller
Using the classification of -dimensional manifolds by Wall, Jupp and Žubr, we observe that the diffeomorphism type of simply-connected, compact -dimensional integer GKM …
Symplectic and Kähler structures on biquotients
Oliver Goertsches, Panagiotis Konstantis, Leopold Zoller
We construct symplectic structures on roughly half of all equal rank biquotients of the form , where is a compact simple Lie group and a torus, and investigate Hamilt…
Equivariant de Rham Cohomology: Theory and Applications
Oliver Goertsches, Leopold Zoller
This is a survey on the equivariant cohomology of Lie group actions on manifolds, from the point of view of de Rham theory. Emphasis is put on the notion of equivariant formality,…
New bounds on the toral rank with application to cohomologically symplectic spaces
Leopold Zoller
We use Boij-Söderberg theory to give two lower bounds for the dimension of the cohomology of a finite CW-complex in terms of the toral rank and certain Betti numbers of the space.…