위상수학II 강의록 페이지입니다.



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made by 김명일,김선영(2001년), 김선화,이주현,하정완 (2004년)

추가및 수정 김태경 (2009년1학기)

  1. Manifolds and Classification of Surface
    1. Manifolds
      Definition and examples [ps] [pdf] [TeX]
      Basic topological properties [ps] [pdf] [TeX]
      Further examples [ps] [pdf] [TeX]
      * Manifold with boundary [ps] [pdf] * 1-manifold [ps] [pdf] [TeX]
    2. Compact Surface
      Introduction [ps] [pdf] [pdf old version including figures] [TeX]
      Compact surface from polygon [pdf] [PDF old version including figures] [TeX]
    3. Orientation and Euler characteristic
      Orientation [PDF] [TeX]
      Euler characteristic of a surface [PDF] [TeX]
      Compact surface with boundary [PDF] [PDF old version including figures] [TeX]

  2. Fundamental group
    1. Definition
      Introduction
      Definition [ps] [pdf] [TeX]
    2. Functorial property
      Functorial property [ps] [pdf] [TeX]
      Homotopy invariance [ps] [pdf] [TeX]
    3. Change of base point
      Base point change [ps] [pdf] [TeX]
      Homotopy invariance(general) [ps] [pdf] [TeX]
    4. Examples
      Contractible space and Brouwer fixed point theorem [ps] [pdf] [TeX]
      Product and Topological group [ps] [pdf] [TeX]

  3. Covering space
    1. Covering space and path lifting property
      Definition and examples [ps] [pdf] [tex]
      Unique path lifting property [ps] [pdf] [tex]
    2. pi_1(S^1) and applications
      Fundamental group of S^1 [ps] [pdf] [tex]
      Applications [ps] [pdf] [tex]
    3. p_# pi_1 (X~, x_0~) and pi_1 - action
      p_# pi_1 (X~, x_0~) [ps] [pdf] [tex]
      pi_1 - action [ps] [pdf] [tex]
    4. General lifting property
      General lifting theorem [ps] [pdf] [tex]
    5. Morphisms and deck transformations
      Morphism between covering spaces [ps] [pdf] [tex]
      Deck transformation group [tex] [pdf]
    6. Existence of covering spaces [ps] [pdf] [TeX] [revised pdf] [revised TeX]
      Existence of universal covering space
      Existence of covering space corresponding to a subgroup
      Applications [pdf] [tex]
    7. Induced covering spaces over a subspace [pdf] [tex]

  4. Simplicial Complex
    1. Simplicial complex in R^n [ps] [pdf] [tex] [revised pdf]
    2. Abstract simplicial complex [ps] [pdf] [tex]
    3. Simplicial map (try) [ps] [pdf] [TeX] (rather than) [ps] [pdf] [tex]
    4. Simplicial approximation theorem [tex] [pdf]
    5. Application [ps] [pdf] [tex]
    6. Edge Path Group [ps] [pdf] [tex]
    7. Van Kampen theorem
    8. Examples [ps] [pdf] [tex]