Up to this point we have obtained results of a very general nature: all n-manifolds embed in ℝ2n+1, all maps can be approximated by C∞ maps, etc. These are useful tools but they give no hint as to how to analyze a particular manifold, or class of manifolds. As yet we are unable even to classify compact 2-manifolds.
KeywordsVector Field Compact Manifold Flow Line Euler Characteristic Integral Curve
Unable to display preview. Download preview PDF.