In this note we investigate about some relations between Poincar\'e dual and other topological objects, such as intersection index, topological degree, and Maslov index of Lagrangian submanifolds. A simple proof of the Poincar\'e-Hopf theorem is recalled. The Lagrangian submanifolds are the geometrical, multi-valued, solutions of physical problems of evolution governed by Hamilton-Jacobi equations: the computation of the algebraic number of the branches is showed to be performed by using Poincar\'e dual.
ON TOPOLOGICAL DEGREE AND POINCARE' DUALITY
CARDIN, FRANCO
1995
Abstract
In this note we investigate about some relations between Poincar\'e dual and other topological objects, such as intersection index, topological degree, and Maslov index of Lagrangian submanifolds. A simple proof of the Poincar\'e-Hopf theorem is recalled. The Lagrangian submanifolds are the geometrical, multi-valued, solutions of physical problems of evolution governed by Hamilton-Jacobi equations: the computation of the algebraic number of the branches is showed to be performed by using Poincar\'e dual.File in questo prodotto:
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