Quadratic forms and Bott periodicity

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Abstract:

Bott periodicity has various formulations in homotopy theory. We present here an interpretation in terms or quadratic forms and symplectic structures. This can be translated in the framework of Quillen's algebraic K-theory for classical groups. We also announce the recent proof of two classical conjectures: the Quillen-Lichtenbaum conjecture in hermitian K-theory and the homotopy limit problem for the orthogonal group. We conclude by some examples of computations.

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