3-MANIFOLDS

Introduction to knots and embeddings. Link diagrams and Alexander polynomial skein relations. Handle decompositions from Morse critical points. Handles as cells. Morse functions from handle decompositions. Handle-bodies and Heegaard diagrams. Fundamental group presentations from Heegaard diagrams. Alexander polynomials from fundamental groups. Fox calculus. Dehn presentations and Kauffman states. Mapping tori and mapping class groups. Nielsen-Thurston classification for mapping class groups. Dehn filling. Dehn surgery. 3-manifolds from Dehn surgery. Seifert fibered spaces. Hyperbolic manifolds. Embedded surface representatives. Incompressible and essential surfaces. Connected sum. JSJ decomposition and geometrization. Turaev torsion and knot decompositions. Foliations. Taut foliations.

  • With Solutions
  • Without Solutions