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I am reading the book on algebraic topology by Fulton and the geometric intusion that is supposed to be given for homological group is the number of connected components.

I wanted to understand an example.

For a circle ( S1) which has got 2 points say A at ( 1, 0) and another point B at ( - 1, 0) is the calculation of the Homology group in the following way

[tex]\stackrel{ a + b }{a -b }[/tex] where a and b are the two generators along the upper half plane and the lower half plane. Then is the result 2a or 2b ie 2*Z.

Thx

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# Computation of homology group

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