- #1
homology
- 306
- 1
Two questions:
(1) What can you mod Z(+)Z by and get Z?
Certainly modding out by Z works, 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 homomorphism f (called the augmentation) between the zero chains C0 and the integers Z, and what f does is to add all the coefficients of the 0-chain together.
Its clear to me that all the zero boundaries are in the kernel of f, 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 less Z than the usual zeroth homology?
Thanks,
Kevin
(1) What can you mod Z(+)Z by and get Z?
Certainly modding out by Z works, 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 homomorphism f (called the augmentation) between the zero chains C0 and the integers Z, and what f does is to add all the coefficients of the 0-chain together.
Its clear to me that all the zero boundaries are in the kernel of f, 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 less Z than the usual zeroth homology?
Thanks,
Kevin