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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…
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…
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…