Schubert cells of mixed type in complex Lagrangian Grassmannians
Abstract
Abstract We describe CW decompositions of complex Lagrangian Grassmannians that contain, as subcomplexes, CW decompositions of real Lagrangian Grassmannians by Schubert–Fuchs cells. The degrees of attaching maps are explicitly computed in terms of quantities that can be read off from the corresponding shifted Young diagrams of mixed type. The signs are determined by a choice of lexicographical ordering on coordinates. As an immediate consequence, we obtain the homotopy extension property for real and complex Lagrangian Grassmannians. We also show that some torsion classes in the integral homology of the real Lagrangian Grassmannian are contractible inside the complex Lagrangian Grassmannian.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Homotopy and Cohomology in Algebraic Topology
Geometric and Algebraic Topology
Publication details
- Journal / source
- Advances in Geometry
- Publisher
- Walter de Gruyter GmbH
- Volume
- 26
- Issue
- 3
- Pages
- 283–301
- Publication date
- 1 July 2026
- Language
- EN