Betti Numbers of Odd Biisotropic Symplectic Grassmannians

We compute the singular cohomology groups of odd biisotropic symplectic Grassmannians $\mathrm{}(k,2n+1)$ by presenting an explicit dimension-preserving combinatorial bijection between the Bialynicki-Birula cells in $\mathrm{}(k,2n+1)$ and the Schubert cells in $\mathrm{Gr}(k,2n+2-k)$.