Topology of the orbit space of a maximal torus action on $\mathrm{Gr}(2,{\mathbb{C}}^5)$

Abstract

In this work, we take a topological approach and introduce a homotopy model of the orbit space of a maximal torus action on $\mathrm{Gr}(2,{\mathbb{C}}^5)$. Using this homotopy model, we compute the integral homology groups and study the homotopy type of the orbit space. More precisely, we endow the homotopy model with a CW complex that contains one top cell and determine the homotopy class of the attaching map of the top cell of the orbit space.