Geodesic
On topological degree and Poincaré duality
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 6 (1995) no. 1, pp. 73-78
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In this Note we investigate about some relations between Poincaré dual and other topological objects, such as intersection index, topological degree, and Maslov index of Lagrangian submanifolds. A simple proof of the Poincaré-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 Poincaré dual. 
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     author = {Cardin, Franco},
     title = {On topological degree and {Poincar\'e} duality},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {73--78},
     year = {1995},
     volume = {Ser. 9, 6},
     number = {1},
     zbl = {0843.58011},
     mrnumber = {MR1340284},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1995_9_6_1_a8/}
}
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Cardin, Franco. On topological degree and Poincaré duality. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 6 (1995) no. 1, pp. 73-78. http://geodesic.mathdoc.fr/item/RLIN_1995_9_6_1_a8/