A De Moivre like Formula for Fixed Point Theory
نویسنده
چکیده
Suppose V is a vectorfield on a compact manifold M with or without boundary ∂M . There is a formula, originally due to Marston Morse [Mo] in 1929, which is not as widely known as it should be. It was rediscovered in 1968 by C. Pugh [P] and by the author [G] in 1985. The formula related the index of the vectorfield V with the index of a vectorfield on part of the boundary. This formula, like de Moivre’s e = cos θ + i sin θ, contains a large amount of information. So let V be a continuous vectorfield on M with no zeros on ∂M . Then
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