Critical Point Theory
In the preceding chapter we set up the two main geometric tools that we shall need in Part III of the book. The first of these are piecewise smooth manifolds of one kind or another, which will serve there as parameter spaces for our random fields, as well as appearing in the proofs. The second are the Lipschitz–Killing curvatures that we met briefly in Chapter 7 and shall look at far more closely, in the piecewise smooth scenario, in Chapter 10. These will appear in the answers to the questions we shall ask. Between the questions and the answers will lie considerable computation, and the main geometric tool that we shall need there is the topic of this short chapter.
KeywordsSimplicial Complex Normal Cone Euler Characteristic Morse Index Morse Theory
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