משטחים: גרפים, חבורות ושימושים

תשע״ח

• הרצאה 1 ←

  Introduction
  Definition of a surface
  Connected sum
  Euler Characteristics of surfaces
  Orientability

• הרצאה 2 ←

  Classification of surfaces:
  
  Dehn - Heegard theorem:
  
  steps of proof:
  
  Reduction to a single equvalence class of vertices
  crosscap normalization (lecture 3)
  Handle normalization (lecture 3)
  from crosscaps and handles to only crosscaps (lecture 3)
  
  
  
  Canonical representation of surfaces
  Seifert - Van Kampen theorem
  Triangulation, Rado theorem

• הרצאה 3 ←

  Classification of surfaces:
  
  steps 2,3,4 of Dehn - Heegard's theorem
  classification of connected compact surfaces with punctures

• הרצאה 4 ←

  The arc complex:
  
  definitions: arcs, essential arcs, arc systems, ambient isotopy, arc complex
  examples of arc complices
  Horer's theorem + corollary

• הרצאה 5 ←

  The arc complex:
  
  definitons: simplicial complex, star, link
  steps in proof of Harer's theorem

• הרצאה 6 ←

  The arc complex:
  
  proof of Harer's theorem
  
  Surffaces and commutator length:
  
  definition of commutator length