A FAMILY OF COMPLEX KLEINIAN SPLIT SOLVABLE GROUPS

The paper proves all three parts of Theorem 1.1: construction of two invariant open sets via stable/unstable projections with a G-equivariant product description (Proposition 2.4), maximality of these domains (Proposition 2.7), and the lattice case (Proposition 3.2 and Section 3) including density of infinite-isotropy points for the lattice and generic accumulation for real points. The model’s approach mirrors the paper’s methods (stable/unstable splitting, Lyapunov-based slices, product structure, properness, and maximality) and gives a valid alternative route to det A(t)=1 via unimodularity. However, in item (3a) the model asserts that every point of Λ has infinite isotropy, which is true for the full Lie group G but does not address (and, if interpreted for Γ, contradicts) the paper’s precise claim that for the discrete lattice Γ the set of points in Λ with infinite isotropy is only dense, not all of Λ. The paper explicitly proves the Γ-version via the characterization z=(I−B^n)^{-1}b and density arguments, whereas the model omits this and conflates G- with Γ-isotropy. Therefore the paper is correct, while the model solution is flawed in (3a). See Theorem 1.1 and its proofs, Proposition 2.4, Proposition 2.7, and the lattice analysis around (3.3)–(3.6) and (3.4) in the paper.