11 citations · 30 across the 20 of their papers we have counts for
22 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…
Almost quaternionic structures on compact rank one symmetric spaces
Oliver Goertsches, Panagiotis Konstantis, Eugenia Loiudice +1
We prove that the only CROSSes that admit a (not necessarily homogeneous) almost quaternionic structure are and .
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 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…
Exotic almost complex circle actions on 6-manifolds
Panagiotis Konstantis, Nicholas Lindsay
Jang has proven a remarkable classification of -dimensional manifolds having an almost complex circle action with fixed points. Jang classifies the weights and associated mu…
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…
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…
A counting invariant for maps into spheres and for zero loci of sections of vector bundles
Panagiotis Konstantis
The set of unrestricted homotopy classes where is a closed and connected spin -manifold is called the -th cohomotopy group of . Moreover it is k…
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 …
Vector bundles and cohomotopies of spin 5-manifolds
Panagiotis Konstantis
The purpose of this paper is two-fold: On the one side we would like to close a gap on the classification of vector bundles over -manifolds. Therefore it will be necessary to st…
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…
Almost complex structures on connected sums of complex projective spaces
Oliver Goertsches, Panagiotis Konstantis
We show that the m-fold connected sum admits an almost complex structure if and only if m is odd.
On the history of the Hopf problem
Ilka Agricola, Giovanni Bazzoni, Oliver Goertsches +2
This short note serves as a historical introduction to the Hopf problem: "Does there exist a complex structure on ?" This unsolved mathematical question was the subject of the…
Almost complex structures on spheres
Panagiotis Konstantis, Maurizio Parton
In this paper we review the well-known fact that the only spheres admitting an almost complex structure are S^2 and S^6. The proof described here uses characteristic classes and th…
Singular oscillatory integrals in equivariant cohomology. Residue formulae for basic differential forms on general symplectic manifolds
Panagiotis Konstantis, Benjamin Küster, Pablo Ramacher
Let be a symplectic manifold and a connected, compact Lie group acting on in a Hamiltonian way. In this paper, we study the equivariant cohomology of represented by…
A note on the topology of irreducible -manifolds
Panagiotis Konstantis
We give necessary and sufficient topological conditions for the existence of an irreducible -structure on a -manifold. Using these conditions we provide some new ex…
Bianchi's classification of 3-dimensional Lie algebras revisited
Manuel Glas, Panagiotis Konstantis, Achim Krause +1
We present Bianchi's proof on the classification of real (and complex) -dimensional Lie algebras in a coordinate free version from a strictly representation theoretic point of v…
A classification of Thurston geometries without compact quotients
Panagiotis Konstantis, Frank Loose
We classify pairs where is a --dimensional simply connected smooth manifold and a Lie group acting on transitively, effectively with compact isotropy group.