- #1
Bacle
- 662
- 1
Hi, All:
Just curious as to the definition of the "mod2 reduction of a homology class".
The context is that an element w in H<sub>2</sub>(M<sup>4</sup>,Z) is called
characteristic if "its mod reduction [w]<sub>2</sub> is Poincare-dual to the
Stiefel-Whitney class w<sub>2</sub> in H<sup>2</sup>(M<sup>4</sup>,Z),
where M<sup>4</sup> is a 4-manifold. Does the reduction just mean that we
start with a Z-chain , and then each coefficient term in the chain is evaluated
mod2?
Thanks.
Just curious as to the definition of the "mod2 reduction of a homology class".
The context is that an element w in H<sub>2</sub>(M<sup>4</sup>,Z) is called
characteristic if "its mod reduction [w]<sub>2</sub> is Poincare-dual to the
Stiefel-Whitney class w<sub>2</sub> in H<sup>2</sup>(M<sup>4</sup>,Z),
where M<sup>4</sup> is a 4-manifold. Does the reduction just mean that we
start with a Z-chain , and then each coefficient term in the chain is evaluated
mod2?
Thanks.