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On the Twisted K-Homology of Simple Lie Groups

Christopher L. Douglas
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Abstract

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-c bordism group of G.

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Christopher L. Douglas. 2008-03-19. On the Twisted K-Homology of Simple Lie Groups. https://arxiv.org/abs/math/0402082

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