Algebraic Topology 代数拓扑与孙悟空72变

How to turn a doughnut to a coffee mug ? They are the ‘same’ (homeomorphic 同胚) when the former is deformed continously into the later (the hole in doughnut becomes the cup’s handle).
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这是孙悟空和二郎神杨戬斗72变法, 老孙输在变庙时, 尾巴变旗杆, 旗在庙后, 被杨戬识破。
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Algebraic Topology: using algebra (eg. Group Theory) to study geometrical shapes.

Difference between Algebraic Topology and Algebraic Geometry (see the previous blog):

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AlgTop1: One-dimensional objects: http://youtu.be/oYFZaqArf54

AlgTop2: Homeomorphism and the group structure on…: http://youtu.be/R_gDV17X7pc

AlgTop3: Two-dimensional surfaces: the sphere: http://youtu.be/tv0XlHfX9r0

AlgTop4: More on the sphere: http://youtu.be/GQ0torqFx8Y

AlgTop5: Two-dimensional objects- the torus and g…: http://youtu.be/4U9XzZjxMFI

AlgTop6: Non-orientable surfaces—the Mobius band: http://youtu.be/vlcdqPWg34k

AlgTop7: The Klein bottle and projective plane: http://youtu.be/ibg5KiG46nk

AlgTop8: Polyhedra and Euler’s formula: http://youtu.be/IY1VyUb44yE

AlgTop9: Applications of Euler’s formula and grap…: http://youtu.be/WxXg49jLkWc

AlgTop10: More on graphs and Euler’s formula: http://youtu.be/AfSBSucXFDM

Continue… (YouTube: search AlgTop11, etc)

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