Homeomorphism between interior dual block complexes and Chevalley exponentiation fibers

Establish that the interior dual block complexes of subword complexes are homeomorphic to the fibers of the Chevalley exponentiation maps to totally nonnegative spaces.

Background

Subword complexes are simplicial complexes associated with words in Coxeter groups. Their interior dual block complexes form combinatorial objects that capture adjacency of strata and subdivision structures. Chevalley exponentiation maps arise in the study of totally nonnegative parts of algebraic groups and related geometric structures.

The cited work [DHM] proposes a conjectural topological relationship linking these combinatorial complexes to the geometry of totally nonnegative spaces via the fibers of the Chevalley exponentiation maps. Verifying this conjecture would bridge combinatorial models from subword complexes with geometric topology of totally nonnegative varieties.