Wall realisation (Ex)
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Exercise 0.1. Given a compact -manifold show that we can attach two -handles to in such a way that the geometric intersection number of immersed spheres representing these handles (i.e. the upper hemisphere, say, is given by the core of the handle und the lower on by a map into ) is for a given , where is some fixed point. \\ Hint: Such a construction is sketched in L¸ck's Article on pages 115 - 116 (and in our talk), all that remains to be checked is the signs.
Hint 0.2. Assume that the cores of the handles are homotopic in .