https://neckpinch.com/authors/timothy-buttsworth/New arXiv papers by Timothy Buttsworth, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2302.04964arxiv:2302.04964Thu, 09 Feb 2023 00:00:00 GMTTheodora Bourni, Timothy Buttsworth, Ramiro Lafuente, Mat Langford — For each n≥ 3, we construct a 'pancake-like', O(2)× O(n-1)-invariant ancient Ricci flow with positive curvature operator and bounded "girth", and we determine its asymptotic limits backwards in time. This solution is new even in dimension three. The construction hinges on the Ricci flow invariance of certain conditions on the curvature and its spatial derivatives under this symmetry regime, whose proof does not follow from Hamilton's tensor maximum principle.Ricci flowAncient solutions3-manifoldsSphere theorems https://arxiv.org/abs/2201.09387arxiv:2201.09387Sun, 23 Jan 2022 00:00:00 GMTTimothy Buttsworth, Maximilien Hallgren, Yongjia Zhang — We construct a rotationally invariant Ricci flow through surgery starting at any closed rotationally invariant Riemannian manifold. We demonstrate that a sequence of such Ricci flows with surgery converges to a Ricci flow spacetime in the sense of [32]. Results of Bamler-Kleiner [8] and Haslhofer [29] then guarantee the uniqueness and stability of these spacetimes given initial data. We simplify aspects of this proof in our setting, and show that for rotationally invariant Ricci flows, the closeness of spacetimes can be measured by equivariant comparison maps. Finally we show that the blowup rate of the curvature near a singular time for these Ricci flows is bounded by the inverse of remaining time squared.Ricci flowSingularitiesSurgeryStability & uniquenessRotational symmetry & warped products https://arxiv.org/abs/2111.12807arxiv:2111.12807Wed, 24 Nov 2021 00:00:00 GMTTimothy Buttsworth — Using center manifolds and topological degree theory, we construct a new family of complete, SU(2)-invariant and steady gradient Ricci solitons on the four-dimensional non-compact cohomogeneity one manifold with group diagram ℤ₄⊂ U(1)⊂ SU(2). We also provide simpler constructions of the existing U(2)-invariant steady and complete gradient solitons on the cohomogeneity one manifolds with group diagrams ℤₙ⊂ U(1)⊂ SU(2) for any n∈ ℕ, including Appleton's non-collapsed solitons for n≥ 3.Ricci solitons(Non)collapsing4-manifoldsHomogeneous spacesBoundaries & non-compact