Pith. sign in

REVIEW 2 cited by

Computer proofs for Property (T), and SDP duality

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2009.05134 v3 pith:BDH5DBFJ submitted 2020-09-10 math.GR math.OA

Martin Nitsche This is my paper · ORCID
classification math.GRmath.OA
keywords propertycocyclescomputerdualitygeometricprogramsproofssimplify
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

We show that the semidefinite programs involved in the computer proofs for Kazhdan's property (T) satisfy strong duality and that the dual programs have a geometric interpretation in terms of harmonic cocycles. By dualizing geometric arguments about cocycles, we are able to simplify the property (T) SDP in the case where it carries a symmetry by finite-order inner automorphisms. As an application, we simplify the SDP proof for $SL(n,\mathbb{Z})$ and we prove that $Aut(F_4)$ has property (T).

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Abelianizations of finite-index subgroups of the handlebody group

    math.GT 2026-07 accept novelty 6.0 of 10

    For genus ≥ 4, meridian multitwists vanish in H_1 of any finite-index subgroup of the handlebody group, and subgroups containing the Torelli group, twist group, or Johnson kernel have trivial rational abelianization.

  2. Inducing spectral gaps for the cohomological Laplacians of $\operatorname{Sp}_{2n}(\mathbb{Z})$

    math.GR 2025-04 conditional novelty 6.0 of 10

    An induction result reduces the spectral gap problem for the cohomological Laplacian of Sp_{2n}(Z) to a base case, and computer-assisted checks give lower bounds for quotients and small n.

Pith tools