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arxiv: math/0402082 · v4 · submitted 2004-02-05 · 🧮 math.AT · math.KT

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On the Twisted K-Homology of Simple Lie Groups

Christopher L. Douglas
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classification 🧮 math.AT math.KT
keywords grouptwistedcyclick-homologyordersimplealgebraalong
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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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  1. Unraveling the Bott spiral

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    A new homotopy model for the Bott spiral of fermionic SPTs is built via twisted ABS orientation and IFT spiral maps, showing IFTs need more symmetry data than K-theory and relying on an extraspecial group isomorphism ...