Published paper
Abstract
The paper gives a quantitative recurrence alternative for unipotent trajectories in arithmetic homogeneous spaces and develops the reduction-theoretic compactness criterion used in later non-divergence arguments.
Role in dependence graphs
Proof-critical source
The Dirichlet spectrum
This paper is included only for the following marked statement:
- Proposition 1.8 · Proceedings of the Indian Academy of Sciences 101 (1991), printed p. 8Compactness of the quotient set defined by an admissible parabolic sequence and two-sided reduction-function bounds.
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Exact reviewed source
Exact IAS repository publisher scan · Proceedings of the Indian Academy of Sciences 101 (1991), 1–17
S. G. Dani and G. A. Margulis. Asymptotic behaviour of trajectories of unipotent flows on homogeneous spaces. Proceedings of the Indian Academy of Sciences - Mathematical Sciences 101 (1991), 1–17.
Open audited source ↗01Statements2 reported findingsNo statement issues found
Proposition 1.8 correctly identifies the compact quotient set determined by a fixed parabolic index set and two-sided bounds on the reduction functions.
Proposition 1.8No issue found
The compact set is independent of the admissible-sequence representative
Printed page 8 · exact publisher scan
Admissibility makes the intermediate parabolic factors telescope modulo the relevant rational subgroup. The inequalities therefore depend only on the final index set and the final coset modulo the lattice, which is the assertion imported as EMS Proposition 3.7.
Proposition 1.3No issue found
The underlying reduction set is relatively compact
Printed pages 6–8 · exact publisher scan
The finite cusp decomposition and lower bounds on all unused simple-root functions confine the split-torus coordinates to a compact range. The remaining factors lie in fixed compact sets and finitely many lattice cosets.
02Proofs2 reported findingsNo proof issues found
The selected compactness argument is complete and uses only the finite reduction-theory decomposition represented by Borel's terminal monograph.
Proof of Proposition 1.3No issue found in the reviewed proof
The induction on admissible sequences closes
Printed pages 6–8
At each step a compact factor moves the current representative into the next rational parabolic. Lower bounds on unused roots and two-sided bounds on used roots then bound every split coordinate. Finiteness of the cusp sets gives relative compactness modulo the lattice.
Proof of Proposition 1.8No issue found in the reviewed proof
Only substitution and lattice-coset invariance are needed
Printed page 8
The proposition follows from the defining admissibility relations and the multiplicativity of the reduction functions; no later unipotent-flow theorem is imported into this selected result.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.