My research lies at the intersection of geometric topology, equivariant topology and toric topology. A recurring theme is the study of manifolds equipped with large transformation groups and the extent to which their topology is determined by their symmetry, orbit-space structure, or homotopy type.

I am particularly interested in rigidity phenomena in toric topology, quaternionic analogues of toric geometry, moment-angle manifolds and polyhedral products, and interactions with surgery theory, nonpositive curvature, and geometric group theory.

Preprints:

• P. Batakidis & I. Gkeneralis. “Obstructions to lifting quaternionic torus actions”. (submitted) [arXiv]
• I. Gkeneralis. “Equivariant rigidity of complex and quaternionic moment-angle manifolds“. (submitted) [arXiv]
• I. Gkeneralis. “Remarks on topological rigidity of real moment-angle manifolds“. (submitted) [arXiv]
• P. Batakidis & I. Gkeneralis. “The topology of local quaternionic toric actions“. (submitted) [arXiv]

Publications:

• P. Batakidis & I. Gkeneralis. “Tetraplectic structures compatible with local quaternionic toric actions“. Ann. Global Anal. Geom. 69, 1 (2026), no. 1, 28 pp. [arXiv] [journal]
• I. Gkeneralis & E. Prassidis. “Topological rigidity of quoric manifolds“. Colloq. Math. 179 (2025), no. 1, 1-19. [arXiv] [journal]