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Generic Intersection of non-planar Surfaces in R^4

  1. Apr 18, 2010 #1
    Hi, everyone:

    How do we show that 2 planar surfaces in R^4 intersect at points (possibly empty

    sets of points, but not in lines, etc.).

    I am curious to see how we justify the Poincare dual of the intersection form in

    cohomology being modular, i.e., integer-valued.?

    I am confused because the same does not seem to apply to, e.g., lines, which,

    when embedded in R^2 or R^3 and R^4 , intersect (if at all) at points.

  2. jcsd
  3. Apr 19, 2010 #2
    It's transversality. If the intersection is transverse, they intersect in a submanifold with the appropriate dimension (dim A +dim B - dim M). Here the dimension is 0, so they generically intersect in isolated points, if at all.
  4. Apr 20, 2010 #3
    Just to say thanks, Zhentil; you have been very helpful.
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