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KRISTIAN JONSSON MOI (Kopenhagen): Deloopings in Real algabraic K-theory (06/05/2014)


I will discuss the algebraic K-theory exact categories with duality, such as the category of finite dimensional vector spaces over a field with the usual duality. In such a category it makes sense to talk about symmetric bilinear forms and the K-theory of these is given by the Grothendieck-Witt space GW(C) of C. Recently Hesselholt and Madsen have defined real algebraic K-theory which to an exact category C with duality associates a C_2-equivariant space KR(C) defined by a construction similar to Waldhausen's S-construction. Its underlying space is homotopy equivalent to the usual algebraic K-theory space of C. I will report on a recent equivariant delooping theorem for the space KR(C) and describe the connections between KR(C), GW(C) and classical invariants of C such as Witt groups and Grothendieck-Witt groups.

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