Linking and Morse Theory
نویسندگان
چکیده
A. In this paper we use Morse theory and the gradient flow of a Morse-Smale function to compute the linking number of a two-component link L in S 3 , by counting the signed number of gradient flow lines passing through each component of L. We will also use three Morse-Smale functions and their gradient flows, to compute Milnor's triple linking number of three-component links by counting flow trees with sign. C 1. Introduction 1 2. Background notions 2 2.1. Morse theory 3 2.2. Stable and unstable manifolds 6 2.3. Morse homology 8 2.4. Transversality 9 3. Linking number 10 4. Milnor's triple linking number 15 References 17
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