https://neckpinch.com/authors/john-hughes/New arXiv papers by John Hughes, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2509.23276arxiv:2509.23276Sat, 27 Sep 2025 00:00:00 GMTJohn Hughes — This paper proves that there exists a non-trivial ancient solution to the Ricci flow emerging from the Taub-Bolt metric.Ricci flowAncient solutions https://arxiv.org/abs/2509.23257arxiv:2509.23257Sat, 27 Sep 2025 00:00:00 GMTJohn Hughes — This paper shows for the first time the existence of a Ricci flow with surgery with local topology change \mathbbCP^2\setminus\{ pt\} \rightarrow \mathbbR^4. The post surgery flow converges to the Taub-NUT metric on \mathbbR^4 in infinite time.Ricci flowSingularitiesSurgery https://arxiv.org/abs/2408.15269arxiv:2408.15269Mon, 12 Aug 2024 00:00:00 GMTJohn Hughes — In this paper we prove that there exists a compact perturbation of the Ricci flat Taub-Bolt metric that evolves under the Ricci flow into a finite time singularity modelled on the shrinking solition FIK [5]. Moreover, this perturbation can be made arbitrarily L^2-small with respect to the Taub-Bolt metric. The method of proof closely follows the strategy adopted in [14], where the author constructs, via a Ważewski box argument, Ricci flows on compact manifolds which encounter finite singularities modelled on a given asymptotically conical shrinking soliton.Ricci flowRicci solitonsRicci-flat & Calabi–YauSingularitiesBoundaries & non-compact