Two questions:(adsbygoogle = window.adsbygoogle || []).push({});

(1) What can you modZ(+)Zby and getZ?

Certainly modding out byZworks, but does anything else?

(2) I've just started reading about reduced homology (in particular the reduced zeroth homology (singular). So as a refresher: We define a homomorphismf(called the augmentation) between the zero chains C_{0}and the integersZ, and whatfdoes is to add all the coefficients of the 0-chain together.

Its clear to me that all the zero boundaries are in the kernel off, but why wouldn't it always be equal to it?

Another way of asking this is to say: why doesn't the reduced zeroth homology just have one lessZthan the usual zeroth homology?

Thanks,

Kevin

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# Reduced homology

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