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

추가및 수정 김태경 (2009년1학기)

- Manifolds and Classification of Surface

- 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] - Compact Surface

Introduction [ps] [pdf] [pdf old version including figures] [TeX]

Compact surface from polygon [pdf] [PDF old version including figures] [TeX] - 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]

- Manifolds
- Fundamental group

- Definition

Introduction

Definition [ps] [pdf] [TeX] - Functorial property

Functorial property [ps] [pdf] [TeX]

Homotopy invariance [ps] [pdf] [TeX] - Change of base point

Base point change [ps] [pdf] [TeX]

Homotopy invariance(general) [ps] [pdf] [TeX] - Examples

Contractible space and Brouwer fixed point theorem [ps] [pdf] [TeX]

Product and Topological group [ps] [pdf] [TeX]

- Definition
- Covering space

- Covering space and path lifting property

Definition and examples [ps] [pdf] [tex]

Unique path lifting property [ps] [pdf] [tex] - pi_1(S^1) and applications

Fundamental group of S^1 [ps] [pdf] [tex]

Applications [ps] [pdf] [tex] - 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] - General lifting property

General lifting theorem [ps] [pdf] [tex] - Morphisms and deck transformations

Morphism between covering spaces [ps] [pdf] [tex]

Deck transformation group [tex] [pdf] - 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] - Induced covering spaces over a subspace [pdf] [tex]

- Covering space and path lifting property
- Simplicial Complex

- Simplicial complex in R^n [ps] [pdf] [tex] [revised pdf]
- Abstract simplicial complex [ps] [pdf] [tex]
- Simplicial map (try) [ps] [pdf] [TeX] (rather than) [ps] [pdf] [tex]
- Simplicial approximation theorem [tex] [pdf]
- Application [ps] [pdf] [tex]
- Edge Path Group [ps] [pdf] [tex]
- Van Kampen theorem
- Examples [ps] [pdf] [tex]