发表机构
Institut für Mathematik und Informatik der Universität Greifswald（格赖夫斯瓦尔德大学数学与信息学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推广Baum-Douglas-Taylor的结果，利用正则边界条件的系统方法，将局部边界条件定义的K-同调循环推广到任意阶椭圆算子及非紧致流形，并证明在更强正则性下可定义绝对K-同调类。
AI 中文摘要
在其开创性工作中，Baum-Douglas-Taylor证明了在某一紧致性假设下，紧致带边流形上一阶椭圆算子的局部边界条件定义了相对K-同调的循环。利用正则边界条件的系统方法，我们将他们的结果推广到任意阶椭圆算子以及具有可能非紧致边界的非紧致流形上。此外，我们证明在更强的正则性条件下，局部边界条件甚至定义了绝对K-同调的循环。与相对类不同，所得的绝对K-同调类通常不独立于边界条件的选择。
英文摘要
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.
