MATRIX 2019 Interactions: Exercises
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== Invariants of knots from Heegaard Floer homology == | == Invariants of knots from Heegaard Floer homology == | ||
+ | === Lecture 1: Heegaard diagrams === | ||
+ | === Lecture 2: Floer homology === | ||
+ | === Lecture 3: Knot Floer homology === | ||
+ | === Lecture 4: The Upsilon invariant === | ||
+ | === Lecture 5: Further applications === | ||
[[Category:MATRIX 2019 Interactions]] | [[Category:MATRIX 2019 Interactions]] |
Revision as of 13:57, 6 January 2019
This page lists the exercises for consideration during the MATRIX 2019 Interactions meeting.
Participants are encouraged to work on the exercises and contribute solutions on the discussion page.
Contents |
1 Surgery: high-d methods in low-d
1.1 Normal maps and the surgery obstruction
- Stability of vector bundles (Ex)
- Normal maps - (non)-examples (Ex)
- Immersing n-spheres in 2n-space (Ex)
- Surgery obstruction, signature (Ex)
- Surgery obstruction, Arf-invariant (Ex)
2 The (stable) Cannon Conjecture
2.1 Lecture 1: An introduction to 3-manifolds
- Betti numbers of 3-manifolds (Ex)
- Non-prime solvable fundamental groups (Ex)
- Atoroidal 3-manifolds (Ex)
- Three dimensional Heisenberg group (Ex)
- Circle actions on 3-manifolds (Ex)
2.2 Lecture 2: An introduction to hyperbolic groups
- Torsion-free solvable hyperbolic groups (Ex)
- Fundamental groups of surfaces (Ex)
- Minimal dimension of BG (Ex)
- Extensions of groups (Ex)
- Boundaries of Fuchsian groups (Ex)