与离散群相关的椭圆算子的局域陈氏特征与索引

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI:10.1134/S1061920824040174

H.H. Abbas, A.Yu. Savin

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引用次数: 0

摘要

给定无限离散群对光滑流形的作用，构造了群中不动点子流形上等变向量束交叉积的循环上同调的等变Chern特征。利用这个陈氏特征，我们得到了与群作用相关的非局部椭圆算子的一个索引公式。DOI 10.1134 / S1061920824040174

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Localized Chern Character and the index of Elliptic Operators Associated with Discrete Groups

Given an action of an infinite discrete group on a smooth manifold, we construct an equivariant Chern character in cyclic cohomolgy of the crossed product for equivariant vector bundles over fixed point submanifolds of torsion elements in the group. We use this Chern character to obtain an index formula for nonlocal elliptic operators associated with the group action.

DOI 10.1134/S1061920824040174

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.