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arXiv · 1904.04069

A geometric approach to K-homology for Lie manifolds

Karsten Bohlen·Jean-Marie Lescure
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Abstract

We show that the computation of the Fredholm index of a fully elliptic pseudodifferential operator on an integrated Lie manifold can be reduced to the computation of the index of a Dirac operator, perturbed by a smoothing operator, canonically associated, via the so-called clutching map. To this end we adapt to our framework ideas coming from Baum-Douglas geometric $K$-homology and in particular we introduce a notion of geometric cycles, that can be categorized as a variant of the famous geometric $K$-homology groups, for the specific situation here. We also define a comparison map between this geometric $K$-homology theory and a relative $K$-theory group, directly associated to a fully elliptic pseudodifferential operator.

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Karsten Bohlen, Jean-Marie Lescure. 2019-04-05. A geometric approach to K-homology for Lie manifolds. https://arxiv.org/abs/1904.04069

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