As on arXiv
Abstract
In the following work, an attempt to conciliate the Ricci flow conjecture and the Cobordism conjecture, stated as refinements of the Swampland distance conjecture and of the No global symmetries conjecture respectively, is presented. This is done by starting from a suitable manifold with trivial cobordism class, applying surgery techniques to Ricci flow singularities and trivialising the cobordism class of one of the resulting connected components via the introduction of appropriate defects. The specific example of is studied in detail. A connection between the process of blowing up a point of a manifold and that of taking the connected sum of such with is explored. Hence, the problem of studying the Ricci flow of a whose cobordism class is trivialised by the addition of copies of is tackled by applying both the techniques developed in the previous sections and the classification of singularities in terms of ADE groups.
Comments: 52 pages, 2 figures
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
-
Gradient flow of Einstein-Maxwell theory and Reissner-Nordström black holes
Topics Singularities · Same authors Davide De Biasio, Dieter Lust
-
Navigating string theory field space with geometric flows
Topics Ricci flow · Same author Dieter Lust · Shared terms “Flow Conjecture”, “Distance Conjecture”, “Swampland Distance”
-
Towards a Taub-Bolt to Taub-NUT via Ricci flow with surgery
Topics Surgery, Singularities
-
Mean convex flows with surgery
Topics Surgery, Singularities
-
Classification of compact manifolds with positive isotropic curvature
Topics Surgery · Shared terms “connected sum”, “following”
-
On-Shell Flow
Topics Ricci flow · Same author Davide De Biasio · Shared terms “Swampland Distance”, “Distance Conjecture”
-
Passing through nondegenerate singularities in mean curvature flows
Topics Surgery, Singularities
-
Open manifolds with uniformly positive isotropic curvature
Topics Surgery, Singularities · Shared terms “connected sum”, “following”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 12B.5The Canonical Neighbourhood Theorem
Every high-curvature point looks like a neck or a cap.
- 12B.7The Singular Time: Horns and Strong Necks
The limit metric at a singular time, the set Ω where curvature stays bounded, ε-horns and their ends, and strong δ-necks deep in a horn, following Perelman II §3 and Morgan–Tian chapter 11.
- 12B.12Canonical Neighbourhoods After Surgery
The strong canonical neighbourhood assumption justified across surgeries: the blow-up argument, the three cases for a limit that meets a surgery, and the choice of δ (Perelman II §5; Morgan–Tian chapter 17).