H omotopy and The Fundamental Groups
5
Homotopy and The Fundamental Groups ---Jue Wang ---Math 480
description
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: - PowerPoint PPT Presentation
Transcript of H omotopy and The Fundamental Groups
Homotopy and The Fundamental Groups
---Jue Wang---Math 480
HOMOTOPY
HOMOTOPY
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.
The FUNDAMENTAL GROUP