Goal: learn about tools for constructing and working with 3-manifolds.

Meeting time: Fridays 1-2pm in PMA 9.166

Schedule

• (Feb 02) Heegaard splittings — Abhishek
• (Feb 09) Dehn surgery + filling 1 — Remy
• (Feb 16) Dehn surgery + filling 2 — Shiyu
• (Feb 23) Branched coverings — Audrick
• (Mar 01) —
• (Mar 08) —
• (Mar 15) Spring break
• (Mar 22) -
• (Mar 29) JSJ decomposition and Seifert fibered manifolds — Aru
• (Apr 05) Geometrization — Luis
• (Apr 12) -
• (Apr 19) Hyperbolic 3-manifolds — Winston
• (Apr 26) TBD

Possible further topics

• Hyperbolic 3-manifolds (Mostow rigidity, Haken manifolds, incompressible surfaces, hyperbolic Dehn surgery)
• Contact structures
• Foliations/fibrations
• Quantum invariants
• Smale conjecture

Resources

• Heegaard splittings, Dehn surgery, branched coverings:
  • Rolfsen - Knots and Links
  • Schultens - Introduction to 3-manifolds
  • Saveliev - Lectures on the Topology of 3-manifolds
• Prime decomposition, Seifert fibered spaces, JSJ decomposition:
  • Hatcher - Basic 3-Manifold Topology
  • Martelli - An introduction to geometric topology
  • Lackenby - Three-dimensional manifolds
  • Schultens - Introduction to 3-manifolds
• Geometrization, hyperbolic 3-manifolds
  • Scott - The Geometries of 3-Manifolds
  • Martelli - An introduction to geometric topology
  • Thurston's notes - The Geometry and Topology of 3-Manifolds
  • Purcell - Hyperbolic Knot Theory