Math 6833     Geometric Group Theory         Fall 1999

 

Information and Messages

  • The Math 6833 course announcement.
  • Math 6833 grading policy.
  • Office hours are by appointment or email.
  • We now meet in 928PHSC on Tu/Th 9:00--10:15am.
  • List of topics (this will grow). Current one is highlighted.
    • Fundamental group.
    • Free groups, presentations of groups, generators and relations,
      Tietze transformations, examples.
    • Free products, free products with amalgamation, push outs.
    • Seifert-Van Kampen theorem and applications: knot complements,
      Dehn presentation (and complex), Wirtinger presentation,
      Torus knot presentations, classifying torus knots
    • CW complexes, simplicial complexes, piecewise euclidean polyhedral complexes,
      piecewise hyperbolic polyhedral complexes, presentation 2-complexes.
    • Covering spaces, lifting properties, classification of covering spaces,
      deck transformations and group actions.
    • HNN extensions and free products with amalgamation: topology, group theory, examples.
      Normal forms, embedding theorems.
    • Grushko and Kurosh theorems. Applications.
    • Graphs of groups, graphs of spaces; groups acting on graphs, Bass-Serre theorems.

     
  • Student seminar talks:
     
    Date Venue and Time Speaker Topic
    Thu
    Sep. 16    		 928 PHSC
    9:00am     		Lourdes
    Juan    		 Homotopy equivalences and isomorphisms
    Thu
    Sep. 16    		 928 PHSC
    9:40am     		Marius
    Munteanu    		 Open coverings and homotopy type -- examples
    Tue
    Oct. 12    		 928 PHSC
    9:00am     		Russ
    Goodman    		 The Wirtinger persentation of link complement groups
    Mon
    Nov. 1    		 928 PHSC
    9:35am     		Marius
    Munteanu    		 Ideal tetrahedral decomposition of the figure eight knot complement
    Fri
    Nov. 12    		 928 PHSC
    9:35am     		Russ
    Goodman    		 Ambient isotopies and mirror images of torus knots
    Fri
    Dec 3    		 928 PHSC
    9:35am     		Lourdes
    Juan     		Stalling's: Topology of finite graphs I
    Mon
    Dec 6    		 928 PHSC
    9:35am     		Russ
    Goodman     		Stalling's: Topology of finite graphs II
    Wed
    Dec 8    		 928 PHSC
    9:35am     		Lourdes
    Juan     		Stalling's: Topology of finite graphs III
    Fri
    Dec 10    		 928 PHSC
    9:35am     		Marius
    Munteanu    		 Menasco's ideal polyhedral decompositions of link complements