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I'd like some help understanding three things.
- What is the topology of the Grassmann manifold or oriented 2-planes in R^4?
- What is the Euler class of the canonical oriented 2 plane bundle over it?
- I think that the Euler class of the normal bundle of an oriented surface in R^4 is zero. Is the normal bundle always trivial?
- What is the topology of the Grassmann manifold or oriented 2-planes in R^4?
- What is the Euler class of the canonical oriented 2 plane bundle over it?
- I think that the Euler class of the normal bundle of an oriented surface in R^4 is zero. Is the normal bundle always trivial?
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