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).

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。

Algebraic Topology: using algebra (eg. Group Theory) to study geometrical shapes.

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


AlgTop1: One-dimensional objects:

AlgTop2: Homeomorphism and the group structure on…:

AlgTop3: Two-dimensional surfaces: the sphere:

AlgTop4: More on the sphere:

AlgTop5: Two-dimensional objects- the torus and g…:

AlgTop6: Non-orientable surfaces—the Mobius band:

AlgTop7: The Klein bottle and projective plane:

AlgTop8: Polyhedra and Euler’s formula:

AlgTop9: Applications of Euler’s formula and grap…:

AlgTop10: More on graphs and Euler’s formula:

Continue… (YouTube: search AlgTop11, etc)


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