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Coefficients for commutative K-theory

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OASW02 - Subfactors, higher geometry, higher twists and almost Calabi-Yau algebras

Recently, the study of representation spaces has led to the definition of a new cohomology theory, called commutative K-theory. This theory is a refinement of classical topological K-theory. It is defined using vector bundles whose transition functions commute with each other whenever they are simultaneously defined. I will begin the talk by discussing some general properties of the „classifying space for commutativity in a Lie group“ introduced by Adem-Gomez. Specialising to the unitary groups, I will then show that the spectrum for commutative complex K-theory is precisely the ku-group ring of infinite complex projective space. Finally, I will present some results about the real variant of commutative K-theory.

This talk is part of the Isaac Newton Institute Seminar Series series.

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