Solving the index problem for (curved) Bernstein–Gelfand–Gelfand sequences

IF 0.8 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2026-10-14 DOI:10.1007/s10455-026-10062-3

Magnus Goffeng

引用次数: 0

Abstract

We study the index theory of curved Bernstein–Gelfand–Gelfand (BGG) sequences in parabolic geometry and their role in K-homology and noncommutative geometry. The BGG-sequences fit into K-homology, and we solve their index problem. We provide a condition for when the BGG-complex on the flat parabolic geometry G/P of a semisimple Lie group G fits into G-equivariant K-homology by means of Heisenberg calculus. For higher rank Lie groups, we prove a no-go theorem showing that the approach fails.

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求解（弯曲）Bernstein-Gelfand-Gelfand序列的指标问题

研究了抛物几何中BGG （Bernstein-Gelfand-Gelfand）曲线序列的指标理论及其在k -同调和非交换几何中的作用。bgg -序列符合k -同调，并求解了它们的索引问题。利用Heisenberg演算，给出了半单李群G的平面抛物几何G/P上的bgg -复合体符合G等变k同调的一个条件。对于高阶李群，我们证明了一个no-go定理，表明该方法是失败的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.