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Suites de Sturm, indice de Maslov et periodicite de Bott PDF

205 Pages·2008·2.076 MB·French
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by Jean Barge, Jean Lannes| 2008| 205 pages| 2.076| French

About Suites de Sturm, indice de Maslov et periodicite de Bott

La th?orie classique des suites de Sturm fournit un algorithme pour d?terminer le nombre de racines d’un polyn?me ? coefficients r?els contenues dans un intervalle donn?. L’objet principal de ce m?moire est de montrer qu’une g?n?ralisation ad?quate de la th?orie des suites de Sturm fournit entre autres choses: une notion d’indice de Maslov pour un lacet alg?brique de lagrangiens d?fini sur un anneau commutatif; une d?monstration du th?or?me fondamental de la K-th?orie (alg?brique) hermitienne, th?or?me d? ? M. Karoubi; une d?monstration des th?or?mes de p?riodicit? de Bott (topologique), dans l’esprit des travaux de F. Latour; un calcul du groupe K2 relatif, symplectique-lin?aire, pour tous les anneaux commutatifs, dans l’esprit des travaux de R. Sharpe. Le livre est dans la mesure du possible « self-contained » et ?l?mentaire: il met essentiellement en oeuvre des arguments d’alg?bre lin?aire ou bilin?aire. Il pr?sente une approche unifi?e de l’indice de Maslov en termes de suites de Sturm et de formes quadratiques.

Detailed Information

Author:Jean Barge, Jean Lannes
Publication Year:2008
ISBN:9783764387099
Pages:205
Language:French
File Size:2.076
Format:PDF
Price:FREE
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