The classical theory of Sturm sequences provides an algorithm for determiningthe number of roots of a polynomial with real coefficients contained in an open interval. The main purpose of this monograph is to show that a suitable generalization of the theory of Sturm sequences provides, among others: a notion of Maslov index for an algebraic loop of lagrangians defined over a commutative ring; a proof of the fundamental theorem of (algebraic) hermitian K-theory (theorem due to M. Karoubi); a proof of the theorems of (topological) Bott periodicity (in the spirit of the work of F. Latour); the computation of the relative K2-group, symplectic-linear, for all commutative ring (in the spirit of the work of R. Sharpe). Self-contained and elementary, involving essentially linear and bilinear algebra. Unified approach to the Maslov index using Sturm sequences and quadratic forms. Appeals to both algebraists and topologists INDICE: 1. Introduction. 2. Algèbre linéaire symplectique. 3. Sur la ‘composante connexe’ du point base dans la lagrangienne infinie. 4. Énoncé et démonstration du théorème fondamental de la K-théorie hermitienne. 5. Suites de Sturm et H2 de l'homomorphisme hyperbolique. 6. Généralisations. Références.
- ISBN: 978-3-7643-8709-9
- Editorial: Birkhaüser
- Encuadernacion: Desconocida
- Páginas: 210
- Fecha Publicación: 01/03/2008
- Nº Volúmenes: 1
- Idioma: Inglés