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Page 1: H omotopy and The Fundamental Groups

Homotopy and The Fundamental Groups

---Jue Wang---Math 480

Page 2: H omotopy and The Fundamental Groups

HOMOTOPY

Page 3: H omotopy and The Fundamental Groups

HOMOTOPY

Page 4: H omotopy and The Fundamental Groups

DEFINITION and PROPOSITION

Proposition:The relation of homotopy on paths with fixed base points is an equivalence relation.

Definition:The equivalence class of a path f under the equivalence relation of homotopy is called the homotopy class of f.

Definition:If a path f from I to X with the same starting and ending point, we say it is a loop.

Page 5: H omotopy and The Fundamental Groups

The FUNDAMENTAL GROUP


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