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H omotopy and The Fundamental Groups

H omotopy and The Fundamental Groups. ---Jue Wang ---Math 480. HOMOTOPY. HOMOTOPY. DEFINITION and PROPOSITION. Proposition: The relation of homo t opy on paths with fixed base points is an equivalence relation . Definition:

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H omotopy and The Fundamental Groups

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  1. Homotopy and The Fundamental Groups ---Jue Wang ---Math 480

  2. HOMOTOPY

  3. HOMOTOPY

  4. DEFINITION and PROPOSITION • Proposition: • The relation of homotopyon 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.

  5. TheFUNDAMENTAL GROUP

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