Work

A Lean Formalization of the Hamilton--Perelman Proof of the Three-Dimensional Poincaré Conjecture

Year: 2026

Type: preprint

Abstract: We formalize the smooth three-dimensional Poincaré conjecture, together with the Moise smoothing theorem, yielding the topological three-dimensional Poincaré conjecture. The smooth proof follows the Hamilton--Perelman route through Ricci flow with surgery and finite-time extinction.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.33842

Authors: Qin, Ziyang, Liao, Yuan, Khaitan, Ayush, Chow, Bennett

Institutions: Cornell University, University of California San Diego, Princeton University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Defense Advanced Research Projects Agency

OpenAlex ID: W7214762756

Cites:

Cited by: 1

Related to: 10