Regular boundary conditions and analytic K-homology

Alexander Engel; Matti Lyko

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arXiv · 2610.02899

Regular boundary conditions and analytic K-homology

Alexander Engel·Matti Lyko

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Abstract

In their seminal work, Baum-Douglas-Taylor showed that under a certain compactness assumption, local boundary conditions for first-order elliptic operators over compact manifolds with boundary define cycles for relative K-homology. Using a systematic approach to regular boundary conditions, we generalize their result to elliptic operators of arbitrary order and to non-compact manifolds with potentially non-compact boundary. In addition, we show that under stronger regularity conditions, local boundary conditions even define cycles for absolute K-homology. In contrast to the relative classes, the resulting absolute K-homology classes are in general not independent of the choice of boundary condition.

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Alexander Engel, Matti Lyko. 2026-10-02. Regular boundary conditions and analytic K-homology. https://arxiv.org/abs/2610.02899

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