Schubert calculus on the grassmannian of hermitian lagrangian spaces

Details Schubert calculus on the grassmannian of hermitian lagrangian spaces Schubert calculus on the grassmannian of hermitian lagrangian spaces

2007-08-20

arxiv.org/abs/0708.2669v3

Mathematics

Geometric Topology

52 pages, 1 figure. Fixed typos, added new references

Scientific paper

The grassmannian of hermitian lagrangian spaces in $\mathbb{C}^n\oplus \mathbb{C}^n$ is a natural compactification of the space of hermitian $n\times n$ matrices. We describe a Schubert-like, Whitney regular stratification on this space which has a Morse theoretic origin. We prove that these strata define closed subanalytic currents \`{a} la R. Hardt, generating the integral homology of this space, we investigate their intersection theoretic properties, and we prove certain odd (in K-theoretic sense) Thom-Porteous type theorems.

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