On the twisted K-homology of simple Lie groups

By Christopher L. Douglas. 2004

58 citations recorded by the source corpus.

We prove that the twisted K-homology of a simply connected simple Lie group G of rank n is an exterior algebra on n-1 generators tensor a cyclic group. We give a detailed description of the order of this cyclic group in terms of the dimensions of irreducible representations of G and show that the congruences determining this cyclic order lift along the twisted index map to relations in the twisted Spin bordism group of G.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/433e8a855901d3e53b9554ff3ce3300a7877b037

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In Algebra and Number Theory

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In Mathematical Physics

Citations in the corpus

Parametrized homotopy theory (2004, methodology): “A version of it has been used by Douglas [52] to calculate the twisted K-theory of simply connected simple Lie groups.”
Loop groups and twisted K‐theory I (2007, methodology): “An analog of the spectral sequence (3) has been used by Douglas [15] to compute the (non-equivariant) twisted K-groups K (G) for all simple, simply connected G.”
Geometric cycles, index theory and twisted K-homology (2007, methodology): “wo α-twistedSpinc structures η and η′ on M are called equivalent if there is a homotopy between η and η′. Remark 3.2. (1) Deﬁnition of twisted Spinc manifolds over X is previously given by Douglas in [22] using Hopkins-Singer’s differential cochains developed in [29]. Here in Deﬁnition 3.1, we deﬁne”