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Book 12B

κ-Solutions and Surgery

Perelman, part two

The singularity models in dimension 3, the canonical neighbourhood theorem, and Ricci flow with surgery.

  • Primary sourceRicci flow with surgery on three-manifolds · Grisha Perelman
  • Main companionRicci Flow and the Poincaré Conjecture · Morgan & Tian
In preparation

Contents

  1. 1
    κ-Solutions

    Ancient, nonnegatively curved, noncollapsed: the models for singularities.

    In preparation

  2. 2
    The Structure of κ-Solutions

    Necks and caps, compactness, and universal estimates.

    In preparation

  3. 3
    The Canonical Neighbourhood Theorem

    Every high-curvature point looks like a neck or a cap.

    In preparation

  4. 4
    Surgery

    The standard solution, cutting along necks, and the topology of surgery.

    In preparation

  5. 5
    Ricci Flow with Surgery for All Time

    Choosing the parameters, and why surgeries don’t accumulate.

    In preparation

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