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I am looking for an example of a 4 dimensional compact smooth manifold that has the following properties
- it is orientable
- it can be smoothly embedded in R^8
- its Euler characteristic is odd
- its second Stiefel-Whitney class is zero
- it is orientable
- it can be smoothly embedded in R^8
- its Euler characteristic is odd
- its second Stiefel-Whitney class is zero
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