Topological rigidity of ${\mathrm{SL}}_2$-quotients

TL;DR

This paper explores the topological properties of a specific homogeneous space related to a simple complex algebraic group, calculating invariants and proposing conjectures on its rigidity.

Contribution

It introduces a new topological invariant and formulates conjectures on the space's topological rigidity, advancing understanding in algebraic topology.

Findings

Calculated classical topological invariants of the space

Introduced a new topological invariant

Proposed conjectures on topological rigidity

Abstract

We investigate the homotopy type of a certain homogeneous space for a simple complex algebraic group. We calculate some of its classical topological invariants and introduce a new one. We also propose several conjectures about its topological rigidity.