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Bilkent University

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Undergraduate and Graduate Programs 2020-2021

MATH 612 Fibre Bundles I

A review of homotopy theory; obstruction theory. Vector bundles as a special case of Steenrod bundles; the principal bundle and associated fibrations. Characteristic classes as first obstructions; basic properties, Cartan's formula. The rings of characteristic classes. The splitting principle and further properties. Characteristic classes and manifolds; applications to cobordisms (Thom's theorem). An introduction to Schubert calculus. The topological Riemann-Roch theorem. Credit units: 3 ECTS Credit units: 5.

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